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1999-12-11 03:00:00
2025-04-28 00:58:08
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A000601
Expansion of 1/((1-x)^2*(1-x^2)*(1-x^3)).
[ "1", "2", "4", "7", "11", "16", "23", "31", "41", "53", "67", "83", "102", "123", "147", "174", "204", "237", "274", "314", "358", "406", "458", "514", "575", "640", "710", "785", "865", "950", "1041", "1137", "1239", "1347", "1461", "1581", "1708", "1841", "1981", "2128", "2282", "2443", "2612", "2788", "2972", "3164", "3364", "3572", "3789", "4014" ]
[ "nonn", "easy" ]
132
0
2
[ "A000601", "A002620", "A006148", "A006383" ]
[ "M1043", "N0392" ]
N. J. A. Sloane
2025-03-07T11:53:55
oeisdata/seq/A000/A000601.seq
45464831858c1b550262aca9b5c05d4f
A000602
Number of n-node unrooted quartic trees; number of n-carbon alkanes C(n)H(2n+2) ignoring stereoisomers.
[ "1", "1", "1", "1", "2", "3", "5", "9", "18", "35", "75", "159", "355", "802", "1858", "4347", "10359", "24894", "60523", "148284", "366319", "910726", "2278658", "5731580", "14490245", "36797588", "93839412", "240215803", "617105614", "1590507121", "4111846763", "10660307791", "27711253769" ]
[ "nonn", "easy", "core", "nice", "changed" ]
231
0
5
[ "A000022", "A000200", "A000598", "A000602", "A000625", "A000628", "A067608", "A067609", "A067610", "A144528" ]
[ "M0718", "N0267" ]
N. J. A. Sloane
2025-04-14T11:48:32
oeisdata/seq/A000/A000602.seq
b69420330ef221668c79830842d7a860
A000603
Number of nonnegative solutions to x^2 + y^2 <= n^2.
[ "1", "3", "6", "11", "17", "26", "35", "45", "58", "73", "90", "106", "123", "146", "168", "193", "216", "243", "271", "302", "335", "365", "402", "437", "473", "516", "557", "600", "642", "687", "736", "782", "835", "886", "941", "999", "1050", "1111", "1167", "1234", "1297", "1357", "1424", "1491", "1564", "1636", "1703", "1778", "1852", "1931", "2012", "2095" ]
[ "nonn" ]
52
0
2
[ "A000328", "A000603", "A036695", "A036702", "A255195", "A255238", "A302998" ]
[ "M2541", "N1004" ]
N. J. A. Sloane
2024-07-18T14:29:28
oeisdata/seq/A000/A000603.seq
a1d2320f86f7e8ecd34c06a0c21c1797
A000604
Number of nonnegative solutions to x^2 + y^2 + z^2 <= n^2.
[ "1", "4", "11", "29", "54", "99", "163", "239", "344", "486", "648", "847", "1069", "1355", "1680", "2046", "2446", "2911", "3443", "4022", "4662", "5395", "6145", "6998", "7913", "8913", "10006", "11194", "12437", "13751", "15216", "16710", "18361", "20123", "21950", "23919", "25956", "28150", "30415", "32876", "35385", "38049", "40876" ]
[ "nonn" ]
28
0
2
[ "A000604", "A000606", "A302998" ]
[ "M3419", "N1383" ]
N. J. A. Sloane
2019-09-29T13:06:18
oeisdata/seq/A000/A000604.seq
d7de790c1bcbb5410b3a70905e406c5d
A000605
Number of points of norm <= n in cubic lattice.
[ "1", "7", "33", "123", "257", "515", "925", "1419", "2109", "3071", "4169", "5575", "7153", "9171", "11513", "14147", "17077", "20479", "24405", "28671", "33401", "38911", "44473", "50883", "57777", "65267", "73525", "82519", "91965", "101943", "113081", "124487", "137065", "150555", "164517", "179579", "195269", "212095" ]
[ "nonn" ]
47
0
2
[ "A000605", "A117609", "A302997" ]
[ "M4406", "N1860" ]
N. J. A. Sloane
2019-09-15T13:48:31
oeisdata/seq/A000/A000605.seq
1e9422f42114f839dd1bfb1aee9061e2
A000606
Number of nonnegative solutions to x^2 + y^2 + z^2 <= n.
[ "1", "4", "7", "8", "11", "17", "20", "20", "23", "29", "35", "38", "39", "45", "51", "51", "54", "63", "69", "72", "78", "84", "87", "87", "90", "99", "111", "115", "115", "127", "133", "133", "136", "142", "151", "157", "163", "169", "178", "178", "184", "199", "205", "208", "211", "223", "229", "229", "230", "239", "254", "260", "266", "278", "290", "290", "296" ]
[ "nonn" ]
38
0
2
[ "A000604", "A000606", "A002102", "A117609" ]
[ "M3294", "N1329" ]
N. J. A. Sloane
2022-02-01T01:04:15
oeisdata/seq/A000/A000606.seq
246d5ea2258a55ec18ac4ac782578bdf
A000607
Number of partitions of n into prime parts.
[ "1", "0", "1", "1", "1", "2", "2", "3", "3", "4", "5", "6", "7", "9", "10", "12", "14", "17", "19", "23", "26", "30", "35", "40", "46", "52", "60", "67", "77", "87", "98", "111", "124", "140", "157", "175", "197", "219", "244", "272", "302", "336", "372", "413", "456", "504", "557", "614", "677", "744", "819", "899", "987", "1083", "1186", "1298", "1420", "1552", "1695", "1850", "2018", "2198", "2394", "2605", "2833", "3079", "3344" ]
[ "easy", "nonn", "nice" ]
228
0
6
[ "A000040", "A000041", "A000586", "A000607", "A000720", "A001414", "A004526", "A014689", "A046113", "A046675", "A046676", "A048165", "A051034", "A056768", "A070214", "A112021", "A116865", "A128515", "A192541", "A261013", "A319265", "A319266", "A330953", "A331379", "A331385", "A331387", "A331415", "A331416", "A331417" ]
[ "M0265", "N0093" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000607.seq
c3af4bc342be2f344d35250a0f57df31
A000608
Number of connected partially ordered sets with n unlabeled elements.
[ "1", "1", "1", "3", "10", "44", "238", "1650", "14512", "163341", "2360719", "43944974", "1055019099", "32664984238", "1303143553205", "66900392672168", "4413439778321689" ]
[ "hard", "more", "nonn", "nice" ]
83
0
4
[ "A000112", "A000608", "A263864", "A342500" ]
[ "M2864", "N1152" ]
N. J. A. Sloane, Simon Plouffe, J. A. Wright
2022-09-04T16:49:31
oeisdata/seq/A000/A000608.seq
73406b5988fa1ec7737bc5d423185f57
A000609
Number of threshold functions of n or fewer variables.
[ "2", "4", "14", "104", "1882", "94572", "15028134", "8378070864", "17561539552946", "144130531453121108" ]
[ "nonn", "hard", "core", "nice", "more" ]
92
0
1
[ "A000609", "A000615", "A002077", "A002080", "A109456", "A116986" ]
[ "M1285", "N0492" ]
N. J. A. Sloane
2023-10-30T13:26:26
oeisdata/seq/A000/A000609.seq
66c25d0c6b4a0b1c95b281e70f29d536
A000610
Number of self-complementary Boolean functions of n variables: see Comments for precise definition.
[ "0", "1", "2", "6", "42", "4094", "98210640", "148947659711650464", "872404773126414633407736134582136832", "88627167739308536281147085615274891669779458770791192509009429292662497280" ]
[ "nonn", "nice", "easy", "changed" ]
70
0
3
[ "A000370", "A000610", "A001320", "A317794" ]
[ "M1714", "N0678" ]
N. J. A. Sloane
2025-04-19T18:05:53
oeisdata/seq/A000/A000610.seq
e29aef98b84f753cf6557712ca5df633
A000611
Number of normalized Latin squares of order n containing no 2 X 2 Latin subsquare.
[ "1", "0", "1", "0", "6", "40", "17760", "2096640", "29659631400" ]
[ "nonn", "more" ]
16
1
5
[ "A000611", "A097548", "A097549" ]
null
Brendan McKay
2024-05-19T09:42:14
oeisdata/seq/A000/A000611.seq
a7fadff5802e01efbb60b21caaf96ed7
A000612
Number of P-equivalence classes of switching functions of n or fewer variables, divided by 2.
[ "1", "2", "6", "40", "1992", "18666624", "12813206169137152", "33758171486592987164087845043830784", "1435913805026242504952006868879460423834904914948818373264705576411070464" ]
[ "nonn", "easy", "nice", "core" ]
72
0
2
[ "A000612", "A003180", "A007716", "A055621", "A058891", "A283877", "A300913", "A306005", "A317533", "A317757" ]
[ "M1712", "N0677" ]
N. J. A. Sloane
2024-12-23T11:38:10
oeisdata/seq/A000/A000612.seq
fc9df6d543a960dbd4a4e6550a8827d2
A000613
Number of Boolean functions of n variables.
[ "2", "4", "10", "46", "1372", "475499108", "1038397981840994509577948", "10825608503765473087803384381127710579846422820261084889808" ]
[ "nonn", "easy", "nice" ]
27
1
1
[ "A000585", "A000613" ]
[ "M1241", "N0475" ]
N. J. A. Sloane
2022-10-30T15:43:13
oeisdata/seq/A000/A000613.seq
926824235d6ae16e823c875c9c015e77
A000614
Number of complemented types of Boolean functions of n variables under action of AG(n,2).
[ "2", "3", "6", "18", "206", "7888299", "8112499583888855378066", "42287533217833953489054778023401252726576585396037133766" ]
[ "nonn", "easy", "nice" ]
36
1
1
[ "A000214", "A000614" ]
[ "M0815", "N0307" ]
N. J. A. Sloane
2022-06-17T16:14:39
oeisdata/seq/A000/A000614.seq
8ff1f07cfb976640d7b6de9f44986001
A000615
Threshold functions of exactly n variables.
[ "2", "2", "8", "72", "1536", "86080", "14487040", "8274797440", "17494930604032" ]
[ "nonn", "more" ]
31
0
1
[ "A000609", "A000615" ]
[ "M0379", "N0142", "N0747" ]
N. J. A. Sloane
2023-10-27T03:22:39
oeisdata/seq/A000/A000615.seq
d63f1f5803452b4a447720abded4f683
A000616
a(-1)=1 by convention; for n >= 0, a(n) = number of irreducible Boolean functions of n variables.
[ "1", "2", "3", "6", "22", "402", "1228158", "400507806843728", "527471432057653004017274030725792", "11218076601767519586965281984173341005925142853855481024470471657123840" ]
[ "nonn", "easy", "nice" ]
106
-1
2
[ "A000231", "A000616", "A000618", "A003180", "A039754", "A102449", "A109460", "A109462", "A361870" ]
[ "M0819", "N0310", "N1026" ]
N. J. A. Sloane
2025-01-12T12:12:13
oeisdata/seq/A000/A000616.seq
ddaa083367d5aab9aa5fecdc0fd27cf0
A000617
Number of NP-equivalence classes of threshold functions of n or fewer variables.
[ "2", "3", "5", "10", "27", "119", "1113", "29375", "2730166", "989913346" ]
[ "nonn", "hard", "more", "nice" ]
52
0
1
[ "A000617", "A000619" ]
[ "M0727", "N0272" ]
N. J. A. Sloane
2024-01-04T06:37:43
oeisdata/seq/A000/A000617.seq
cd250b9a4bdcdc74f4304a4f1194e259
A000618
Number of nondegenerate Boolean functions of n variables: For n > 0, a(n) = A000616(n) - A000616(n-1).
[ "2", "1", "3", "16", "380", "1227756", "400507805615570", "527471432057653003616766223882064", "11218076601767519586965281984173341005397671421797828020453197626398048" ]
[ "nonn", "nice" ]
38
0
1
[ "A000371", "A000616", "A000618", "A211705", "A211706" ]
[ "M0160", "N0063" ]
N. J. A. Sloane
2019-10-05T19:50:03
oeisdata/seq/A000/A000618.seq
04747bf6e7ba7b4645e1a45739189f92
A000619
NP-equivalence classes of threshold functions of exactly n variables.
[ "2", "1", "2", "5", "17", "92", "994", "28262", "2700791", "990331318" ]
[ "nonn", "more" ]
47
0
1
[ "A000617", "A000619" ]
[ "M0121", "N0048" ]
N. J. A. Sloane
2023-10-27T03:55:04
oeisdata/seq/A000/A000619.seq
c7ca68d839952c79e7ee4f1cf2f2746a
A000620
Number of monosubstituted alkanes C(n-1)H(2n-1)-X with n-1 carbon atoms that are stereoisomers.
[ "0", "0", "0", "0", "2", "6", "20", "60", "176", "512", "1488", "4326", "12648", "37186", "109980", "327216", "979020", "2944414", "8897732", "27005290", "82288516", "251650788", "772127678", "2376238138", "7333188770", "22688297950", "70360977228", "218678818026", "681017928476", "2124840874610", "6641336507270", "20791999731518" ]
[ "nonn" ]
29
1
5
[ "A000620", "A000621", "A000622", "A000623", "A000624", "A000625", "A239803", "A239805" ]
[ "M1642", "N0642" ]
N. J. A. Sloane
2022-07-18T11:24:24
oeisdata/seq/A000/A000620.seq
052c75641f81d375c80e4522daed1365
A000621
Number of monosubstituted alkanes C(n-1)H(2n-1)-X with n-1 carbon atoms that are not stereoisomers.
[ "1", "1", "1", "2", "3", "5", "8", "14", "23", "39", "65", "110", "184", "310", "520", "876", "1471", "2475", "4159", "6996", "11759", "19775", "33244", "55902", "93984", "158030", "265696", "446746", "751128", "1262940", "2123444", "3570318", "6002983", "10093259", "16970431", "28533590", "47975381", "80664329", "135626284", "228037752" ]
[ "nonn", "nice", "easy" ]
90
1
4
[ "A000620", "A000621", "A000625", "A239804", "A239806" ]
[ "M0697", "N0258" ]
N. J. A. Sloane
2022-06-02T03:29:07
oeisdata/seq/A000/A000621.seq
3c551ea9d527c5fb6a9289d956b614ac
A000622
Number of monosubstituted alkanes C(n)H(2n+1)-X of the form shown in the Comments lines that are stereoisomers.
[ "0", "0", "0", "2", "4", "14", "34", "98", "270", "768", "2192", "6360", "18576", "54780", "162658", "486154", "1461174", "4413988", "13393816", "40807290", "124783604", "382842018", "1178140170", "3635626680", "11247841040", "34880346840", "108402132234", "337576497920", "1053229357732", "3291813720292", "10305275270364" ]
[ "nonn" ]
20
1
4
[ "A000620", "A000622", "A000625", "A239803", "A239807" ]
[ "M1272", "N0490" ]
N. J. A. Sloane
2022-02-01T01:05:20
oeisdata/seq/A000/A000622.seq
b75ce7c276bd1cb3b41304549ace3f00
A000623
Number of monosubstituted alkanes C(n)H(2n+1)-X of the form shown in the Comments lines that are stereoisomers.
[ "0", "0", "0", "0", "0", "0", "6", "18", "66", "208", "646", "1962", "5962", "18014", "54578", "165650", "504220", "1539330", "4713742", "14475936", "44578668", "137634872", "425970290", "1321323952", "4107268140", "12792332438", "39915708564", "124762612530", "390593588402", "1224681912368", "3845387953884", "12090382743374" ]
[ "nonn" ]
21
1
7
[ "A000620", "A000623", "A000625", "A239803", "A239808" ]
[ "M4125", "N1712" ]
N. J. A. Sloane
2022-02-01T01:05:40
oeisdata/seq/A000/A000623.seq
1a26c5295ff5468dac4f29fdf4a7b506
A000624
Number of monosubstituted alkanes C(n)H(2n+1)-X of the form shown in the Comments lines that are not stereoisomers.
[ "0", "0", "0", "1", "1", "3", "4", "9", "13", "26", "40", "74", "118", "210", "342", "595", "981", "1684", "2798", "4763", "7951", "13469", "22548", "38082", "63862", "107666", "180740", "304382", "511292", "860504", "1445998", "2432665", "4088805", "6877172", "11560684", "19441791", "32684789", "54961955", "92404472", "155377371", "261235027" ]
[ "nonn" ]
23
1
6
[ "A000620", "A000624", "A000625", "A239804", "A239809" ]
[ "M2355", "N0932" ]
N. J. A. Sloane
2022-02-01T01:06:00
oeisdata/seq/A000/A000624.seq
4f6979acfed95610bdd0593a045a9326
A000625
Number of n-node steric rooted ternary trees; number of n carbon alkyl radicals C(n)H(2n+1) taking stereoisomers into account.
[ "1", "1", "1", "2", "5", "11", "28", "74", "199", "551", "1553", "4436", "12832", "37496", "110500", "328092", "980491", "2946889", "8901891", "27012286", "82300275", "251670563", "772160922", "2376294040", "7333282754", "22688455980", "70361242924", "218679264772", "681018679604", "2124842137550", "6641338630714", "20792003301836" ]
[ "nonn", "easy", "nice" ]
73
0
4
[ "A000598", "A000602", "A000620", "A000624", "A000625", "A000628", "A010732", "A010733", "A086194", "A086200", "A239803", "A239810" ]
[ "M1402", "N0546" ]
N. J. A. Sloane
2019-02-17T20:45:45
oeisdata/seq/A000/A000625.seq
32d36600f1884d04325eee14c438628b
A000626
Number of stereoisomeric paraffins with n carbon atoms.
[ "0", "0", "0", "0", "0", "0", "4", "11", "35", "101", "290", "804", "2256", "6296", "17689", "49952", "142016", "406330", "1170272", "3390932", "9882412", "28955403", "85261439", "252213192", "749250700", "2234562027", "6688670232", "20088920730", "60525912003", "182895125096", "554186425193", "1683554604984", "5126814324715", "15647846830627", "47862034920652", "146691540312878" ]
[ "nonn" ]
19
1
7
[ "A000626", "A000627", "A000628" ]
[ "M3422", "N1386" ]
N. J. A. Sloane
2022-02-01T01:06:20
oeisdata/seq/A000/A000626.seq
8f659bd224bd5d50216bdb8776f0f75f
A000627
Number of non-stereoisomeric paraffins with n carbon atoms.
[ "1", "1", "1", "2", "3", "5", "7", "13", "20", "35", "55", "96", "156", "267", "438", "747", "1239", "2099", "3498", "5912", "9890", "16677", "27951", "47084", "79019", "133003", "223373", "375824", "631477", "1062160", "1785159", "3002227", "5046641", "8486453", "14266795", "23989770", "40332184", "67816640", "114018876", "191713441", "322330987", "541966582" ]
[ "nonn" ]
20
1
4
[ "A000626", "A000627", "A000628" ]
[ "M0674", "N0249" ]
N. J. A. Sloane
2022-02-01T01:06:37
oeisdata/seq/A000/A000627.seq
5df73e81bdf9bf1d2166be8cd90650a7
A000628
Number of n-node unrooted steric quartic trees; number of n-carbon alkanes C(n)H(2n+2) taking stereoisomers into account.
[ "1", "1", "1", "1", "2", "3", "5", "11", "24", "55", "136", "345", "900", "2412", "6563", "18127", "50699", "143255", "408429", "1173770", "3396844", "9892302", "28972080", "85289390", "252260276", "749329719", "2234695030", "6688893605", "20089296554", "60526543480", "182896187256", "554188210352", "1683557607211", "5126819371356", "15647855317080", "47862049187447", "146691564302648", "450451875783866", "1385724615285949" ]
[ "nonn", "easy", "nice" ]
71
0
5
[ "A000598", "A000602", "A000625", "A000626", "A000627", "A000628", "A010372", "A010373", "A086194", "A086200" ]
[ "M0732", "N0274" ]
N. J. A. Sloane
2025-04-07T11:59:59
oeisdata/seq/A000/A000628.seq
cd7de270fb62934b0c88656e550724b6
A000629
Number of necklaces of partitions of n+1 labeled beads.
[ "1", "2", "6", "26", "150", "1082", "9366", "94586", "1091670", "14174522", "204495126", "3245265146", "56183135190", "1053716696762", "21282685940886", "460566381955706", "10631309363962710", "260741534058271802", "6771069326513690646", "185603174638656822266", "5355375592488768406230" ]
[ "nonn", "easy", "eigen", "nice" ]
305
0
2
[ "A000629", "A000670", "A002050", "A008277", "A008965", "A028246", "A052856", "A052861", "A076726", "A127671", "A241168", "A263634" ]
null
N. J. A. Sloane, Don Knuth, Nick Singer (nsinger(AT)eos.hitc.com)
2025-02-16T08:32:21
oeisdata/seq/A000/A000629.seq
055087dc727aeb15979797a11fd145ac
A000630
Number of ways to represent n using the binary operator a * b = 2^a + b.
[ "1", "1", "2", "3", "7", "12", "23", "41", "81", "149", "282", "522", "987", "1843", "3463", "6473", "12160", "22773", "42719", "80025", "150074", "281258", "527320", "988334", "1852849", "3473061", "6510681", "12204139", "22877649", "42884585", "80389797", "150692973", "282481747", "529522496", "992614937", "1860696007" ]
[ "nonn", "easy", "nice" ]
38
0
3
null
null
N. J. A. Sloane
2021-12-19T09:39:34
oeisdata/seq/A000/A000630.seq
fffa2fcfc7ac7811c4c7090303419c1d
A000631
Number of ethylene derivatives with n carbon atoms.
[ "1", "1", "3", "5", "13", "27", "66", "153", "377", "914", "2281", "5690", "14397", "36564", "93650", "240916", "623338", "1619346", "4224993", "11062046", "29062341", "76581151", "202365823", "536113477", "1423665699", "3788843391", "10103901486", "26995498151", "72253682560", "193706542776" ]
[ "nonn" ]
78
2
3
[ "A000598", "A000631", "A000642", "A027852" ]
[ "M2490", "N0987" ]
N. J. A. Sloane
2020-12-06T14:02:13
oeisdata/seq/A000/A000631.seq
11d4f98c6f740b48721de91ac6953714
A000632
Number of esters with n carbon atoms up to structural isomerism.
[ "1", "2", "4", "9", "20", "45", "105", "249", "599", "1463", "3614", "9016", "22695", "57564", "146985", "377555", "974924", "2529308", "6589734", "17234114", "45228343", "119069228", "314368027", "832193902", "2208347917", "5873364623", "15653499416", "41800070483", "111821751649" ]
[ "nonn" ]
40
2
2
null
[ "M1174", "N0451" ]
N. J. A. Sloane
2025-02-05T10:12:54
oeisdata/seq/A000/A000632.seq
8f0aab67f5b83e70fcc17e16b267bef0
A000633
Number of acyclic quaternary ammonium ions with n carbon atoms.
[ "1", "1", "3", "7", "18", "42", "109", "269", "691", "1759", "4542", "11733", "30559", "79743", "209136", "549959", "1451178", "3838925", "10182703", "27069940", "72121696", "192527888", "514908269", "1379454526", "3701556642", "9947456861", "26770280299", "72138803942", "194638086892", "525773470041", "1421850523472" ]
[ "nonn" ]
27
4
3
[ "A000598", "A000633" ]
[ "M2667", "N1065" ]
N. J. A. Sloane
2023-05-21T22:22:42
oeisdata/seq/A000/A000633.seq
ef08d0a3fe7fcf87945e241c53a7465f
A000634
Number of glycols with n carbon atoms.
[ "1", "2", "6", "14", "38", "97", "260", "688", "1856", "4994", "13550", "36791", "100302", "273824", "749316", "2053247", "5635266", "15484532", "42599485", "117312742", "323373356", "892139389", "2463252315", "6806148956", "18818714543", "52065725034", "144135111504", "399232819042", "1106385615943" ]
[ "nonn" ]
26
2
2
[ "A000634", "A000636", "A000642" ]
[ "M1604", "N0627" ]
N. J. A. Sloane
2018-01-22T19:26:12
oeisdata/seq/A000/A000634.seq
b4009c0e2a8f817bb7cd3c6e921e904a
A000635
Number of paraffins C_n H_{2n} X Y with n carbon atoms.
[ "0", "1", "2", "5", "12", "31", "80", "210", "555", "1479", "3959", "10652", "28760", "77910", "211624", "576221", "1572210", "4297733", "11767328", "32266801", "88594626", "243544919", "670228623", "1846283937", "5090605118", "14047668068", "38794922293", "107215238057", "296501478704" ]
[ "nonn", "easy", "nice" ]
39
0
3
null
[ "M1418", "N0555" ]
N. J. A. Sloane
2021-12-19T09:40:21
oeisdata/seq/A000/A000635.seq
f8c8d4526821228ae2dbc3b61244e7d5
A000636
Number of paraffins C_n H_{2n} X_2 with n carbon atoms.
[ "1", "2", "4", "9", "21", "52", "129", "332", "859", "2261", "5983", "15976", "42836", "115469", "312246", "847241", "2304522", "6283327", "17164401", "46972357", "128741107", "353345434", "970999198", "2671347292", "7356752678", "20279171785", "55948407837", "154479213626", "426845422807", "1180229767202" ]
[ "nonn", "easy", "nice" ]
28
1
2
null
[ "M1185", "N0457" ]
N. J. A. Sloane
2022-01-29T00:59:56
oeisdata/seq/A000/A000636.seq
9740f1aa7e25c3c95f99e203beab2e50
A000637
Number of fixed-point-free permutation groups of degree n.
[ "1", "0", "1", "2", "7", "8", "37", "40", "200", "258", "1039", "1501", "7629", "10109", "54322", "83975", "527036", "780193", "5808293" ]
[ "nonn", "hard", "more", "nice" ]
54
0
4
[ "A000001", "A000019", "A000637", "A000638", "A002106", "A005226", "A005432", "A116693" ]
[ "M1730", "N0685" ]
N. J. A. Sloane
2022-01-29T00:59:44
oeisdata/seq/A000/A000637.seq
1e98c93049f70a13a57cb4cc82c4a7f8
A000638
Number of permutation groups of degree n; also number of conjugacy classes of subgroups of symmetric group S_n; also number of molecular species of degree n.
[ "1", "1", "2", "4", "11", "19", "56", "96", "296", "554", "1593", "3094", "10723", "20832", "75154", "159129", "686165", "1466358", "7274651" ]
[ "nonn", "hard", "more", "nice" ]
83
0
3
[ "A000001", "A000019", "A000637", "A000638", "A005432" ]
[ "M1244", "N0477" ]
N. J. A. Sloane
2023-12-23T14:29:05
oeisdata/seq/A000/A000638.seq
e14297c4b5378a5e309e38c8b804f368
A000639
Number of alkyl benzenes with n carbon atoms: C(n)H(2n-6).
[ "0", "0", "0", "0", "0", "1", "1", "4", "8", "22", "51", "136", "335", "871", "2217", "5749", "14837", "38636", "100622", "263381", "690709", "1817544", "4793449", "12675741", "33592349", "89223734", "237455566", "633176939", "1691377956", "4525792533", "12129365576", "32556355947", "87508275471", "235529797422" ]
[ "nonn", "easy", "nice" ]
42
1
8
[ "A000598", "A000639" ]
[ "M3341", "N1344" ]
N. J. A. Sloane
2022-06-16T23:26:39
oeisdata/seq/A000/A000639.seq
7925d25a9fab3a041bc1c5cf59375752
A000640
Number of paraffins C_n H_{2n-1} XYZ with n carbon atoms.
[ "0", "1", "4", "13", "42", "131", "402", "1218", "3657", "10899", "32298", "95257", "279844", "819390", "2392392", "6967956", "20250974", "58744089", "170118980", "491913999", "1420493862", "4096940530", "11803172152", "33970257473", "97678027311", "280624328431", "805587723862" ]
[ "nonn", "easy" ]
27
0
3
[ "A000598", "A000640", "A000642" ]
[ "M3466", "N1410" ]
N. J. A. Sloane
2021-12-19T09:41:06
oeisdata/seq/A000/A000640.seq
946efda426290bea1a80adbbe532d374
A000641
Number of paraffins C_n H_{2n-1} X_3 with n carbon atoms.
[ "0", "1", "2", "5", "14", "39", "109", "312", "890", "2552", "7325", "21047", "60465", "173750", "499068", "1433071", "4113105", "11799780", "33834367", "96968462", "277771344", "795310628", "2276055442", "6510786627", "18616389094", "53207964655", "152014267327", "434136228215" ]
[ "nonn", "easy" ]
19
0
3
null
[ "M1456", "N0575" ]
N. J. A. Sloane
2022-02-01T01:06:53
oeisdata/seq/A000/A000641.seq
56df966cdc2c8e6ac134570c54546c1a
A000642
a(1)=0; for n>1, a(n) = number of isomeric hydrocarbons of the acetylene series with carbon content n.
[ "0", "1", "1", "2", "3", "7", "14", "32", "72", "171", "405", "989", "2426", "6045", "15167", "38422", "97925", "251275", "648061", "1679869", "4372872", "11428365", "29972078", "78859809", "208094977", "550603722", "1460457242", "3882682803", "10344102122", "27612603765", "73844151259", "197818389539" ]
[ "nonn", "easy", "nice" ]
73
1
4
[ "A000598", "A000642", "A002094" ]
[ "M0839", "N0318" ]
N. J. A. Sloane
2020-11-29T08:18:48
oeisdata/seq/A000/A000642.seq
ef104169d81ed8affc44d636a8989a72
A000643
a(n) = a(n-1) + 2^a(n-2).
[ "0", "0", "1", "2", "4", "8", "24", "280", "16777496", "1942668892225729070919461906823518906642406839052139521251812409738904285205225275672" ]
[ "nonn" ]
21
0
4
[ "A000643", "A000659" ]
null
N. J. A. Sloane
2024-01-05T19:14:02
oeisdata/seq/A000/A000643.seq
677efa586bb4eeaf41d69961dd60281b
A000644
Number of loops of length 4n on square grid that turn at each step and return to start in original direction.
[ "1", "1", "3", "7", "31", "138", "808", "4956", "33047", "227328", "1614793", "11710299", "86495618", "648399937", "4923728056" ]
[ "nonn", "more", "nice", "walk" ]
26
1
3
null
null
N. J. A. Sloane
2022-06-17T03:18:37
oeisdata/seq/A000/A000644.seq
3bf8a57f78e88a7737210284fd73a4db
A000645
Number of alkyls X^{II} C_n H_{2n+1} Y with n carbon atoms.
[ "1", "2", "4", "10", "25", "64", "166", "437", "1157", "3087", "8276", "22287", "60230", "163284", "443820", "1209155", "3300890", "9027337", "24727437", "67829684", "186302693", "512301120", "1410237805", "3885803531", "10716571591", "29579231200", "81704634803", "225845362116" ]
[ "nonn", "easy" ]
19
0
2
null
[ "M1209", "N0467" ]
N. J. A. Sloane
2022-02-01T01:07:09
oeisdata/seq/A000/A000645.seq
3c2829b084c4b6d655dee14468cdf055
A000646
Number of alkyls Y^{II} C_n H_{2n+2} with n carbon atoms.
[ "1", "2", "3", "6", "13", "28", "62", "144", "338", "810", "1970", "4852", "12073", "30334", "76805", "195850", "502461", "1296122", "3359527", "8745744", "22856223", "59944156", "157718380", "416189954", "1101204387", "2920914484", "7765357967", "20688204244", "55225188289", "147688302518" ]
[ "nonn", "easy" ]
18
0
2
null
[ "M0800", "N0303" ]
N. J. A. Sloane
2022-02-01T01:07:23
oeisdata/seq/A000/A000646.seq
750e0581fa9b70041f754294f4eaff30
A000647
Alkyl naphthalenes C_{n+10} H_{2n+8} with n+10 carbon atoms.
[ "1", "2", "12", "32", "110", "310", "920", "2558", "7177", "19660", "53864", "146180", "396296", "1070296", "2888662", "7785856", "20982905", "56536762", "152378548", "410825678", "1108224556", "2991244712", "8079252116", "21837144430", "59066580606", "159886668880", "433122375508" ]
[ "nonn", "easy" ]
17
0
2
null
[ "M2018", "N0798" ]
N. J. A. Sloane
2022-02-01T01:07:41
oeisdata/seq/A000/A000647.seq
8dd5ef85e8bf06c68b5e1718d620dad6
A000648
Number of alkyls C_{n+15} H_{2n+10} (Anthr.) with n carbon atoms.
[ "1", "3", "18", "61", "225", "716", "2272", "6826", "20238", "58552", "167625", "473929", "1330490", "3709591", "10296336", "28466065", "78481065", "215878221", "592832960", "1625887129", "4454936029", "12198071235", "33383810793", "91336813784", "249851178964", "683421422654" ]
[ "nonn", "easy" ]
21
0
2
[ "A000648", "A000649" ]
[ "M3045", "N1235" ]
N. J. A. Sloane
2021-12-19T09:41:37
oeisdata/seq/A000/A000648.seq
34488697e9d82f1f08bea3fd1c2f1fe4
A000649
Number of alkyls C_{n+15} H_{2n+10} (Phenan) with n carbon atoms.
[ "1", "5", "30", "115", "425", "1396", "4440", "13470", "40000", "116140", "332827", "942435", "2647450", "7386925", "20511620", "56731383", "156451985", "430462915", "1182341890", "3243215495", "8887664047", "24338341165", "66616422775", "182276901760", "498657609720", "1364083988834" ]
[ "nonn", "easy" ]
20
0
2
[ "A000648", "A000649" ]
[ "M3958", "N1633" ]
N. J. A. Sloane
2022-02-01T01:07:58
oeisdata/seq/A000/A000649.seq
c482b6f63d4f11721fc0bac28d66354f
A000650
Number of alkyls S C_{n+4} H_{2n+4} with n carbon atoms.
[ "1", "2", "6", "12", "31", "72", "178", "430", "1071", "2654", "6680", "16858", "42926", "109778", "282490", "730028", "1895456", "4940094", "12923600", "33919416", "89301052", "235762572", "624057892", "1655817422", "4403189781", "11733247076", "31326037116", "83786187152", "224475807465" ]
[ "nonn", "easy", "nice" ]
27
0
2
null
[ "M1588", "N0618" ]
N. J. A. Sloane
2021-12-19T09:41:49
oeisdata/seq/A000/A000650.seq
931bbf5655f097b5ffeb83ee8ce9b1c1
A000651
Running time of Takeuchi function.
[ "0", "1", "4", "14", "53", "223", "1034", "5221", "28437", "165859", "1029803", "6772850", "46983238", "342509396", "2615606677", "20865444825", "173446634597", "1499111445237", "13445550920288", "124919896067530", "1200320663197275", "11910845573790488" ]
[ "nonn" ]
41
0
3
[ "A000651", "A143307" ]
null
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000651.seq
377295493638616e5e6b99f70d1eb1e1
A000652
Invertible Boolean functions of n variables.
[ "1", "1", "6", "924", "81738720000", "256963707943061374889193111552000", "30978254928194376001814792318154658399138184007229852126545533479881553257431040000000" ]
[ "nonn", "easy" ]
21
0
3
[ "A000652", "A000653", "A000654", "A000722", "A001038", "A001537", "A046856", "A046857" ]
[ "M4315", "N1807" ]
N. J. A. Sloane
2022-02-01T01:08:43
oeisdata/seq/A000/A000652.seq
85294131ccce19bb43ab4b0825d345b3
A000653
Invertible Boolean functions of n variables.
[ "2", "7", "1172", "36325278240", "18272974787063551687986348306336", "244766458691906180755079840538506099505695351680436638205950721844523539763881615360" ]
[ "nonn" ]
55
1
1
null
[ "M1821", "N0723" ]
N. J. A. Sloane
2023-02-13T03:04:16
oeisdata/seq/A000/A000653.seq
c6adc09620ce51b8e734e995b1a6742f
A000654
Invertible Boolean functions of n variables.
[ "1", "2", "52", "142090700", "17844701940501123640681816160", "59757436204078657410908164193971330396709572693816353610758085074676243846093824" ]
[ "nonn" ]
38
1
2
null
[ "M2173", "N0868" ]
N. J. A. Sloane
2021-02-12T18:16:50
oeisdata/seq/A000/A000654.seq
a961832a303018cd2ae975c4249b227a
A000655
a(n) = number of letters in a(n-1), a(1) = 1 (in English).
[ "1", "3", "5", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4", "4" ]
[ "nonn", "word", "easy" ]
33
1
2
[ "A000655", "A005589", "A061504", "A101432", "A328263" ]
null
N. J. A. Sloane
2024-06-26T09:33:32
oeisdata/seq/A000/A000655.seq
7a9f1b9d8bd9fa77bbd09c9922b727e1
A000656
Invertible Boolean functions of n variables with S(n) acting on the domain and GL(n,2) acting on the range.
[ "2", "3", "56", "43265712", "219289731988435167257927904", "8742218740996073061357349746759733054713953086811227917496519524423937904640" ]
[ "nonn" ]
23
1
1
null
[ "M0924", "N0348" ]
N. J. A. Sloane
2022-02-01T01:09:03
oeisdata/seq/A000/A000656.seq
519c7b0422774cfa4426b469227bc54d
A000657
Median Euler numbers (the middle numbers of Arnold's shuttle triangle).
[ "1", "1", "4", "46", "1024", "36976", "1965664", "144361456", "13997185024", "1731678144256", "266182076161024", "49763143319190016", "11118629668610842624", "2925890822304510631936", "895658946905031792553984", "315558279782214450517374976", "126780706777739389745128013824" ]
[ "nonn", "nice", "easy" ]
94
0
3
[ "A000657", "A002832", "A005799", "A084938", "A098277", "A099023", "A323834" ]
null
N. J. A. Sloane, Don Knuth
2024-11-24T17:11:17
oeisdata/seq/A000/A000657.seq
350bcde13c8a7322d2e33dee7e16a03c
A000658
Strehl's sequence "C_n^(3)".
[ "1", "4", "68", "1732", "51076", "1657904", "57793316", "2117525792", "80483121028", "3147565679824", "125937573689968", "5133632426499152", "212530848994367524", "8914634034287235856", "378138515326996979168", "16196097181014298854032" ]
[ "nonn", "easy", "nice" ]
27
0
2
[ "A000658", "A007318", "A094424" ]
null
Don Knuth
2015-09-09T23:51:09
oeisdata/seq/A000/A000658.seq
850fac7ca5cbbe26da31172af951b7bc
A000659
a(n) = 2^a(n-1) + a(n-2).
[ "0", "0", "1", "2", "5", "34", "17179869189" ]
[ "nonn" ]
16
0
4
[ "A000643", "A000659" ]
null
N. J. A. Sloane
2022-04-09T11:36:51
oeisdata/seq/A000/A000659.seq
64c19e5487369877ec3e03519533fe13
A000660
Boustrophedon transform of 1,1,2,3,4,5,...
[ "1", "2", "5", "14", "41", "136", "523", "2330", "11857", "67912", "432291", "3027166", "23125673", "191389108", "1705788659", "16289080922", "165919213089", "1795666675824", "20576824369027", "248892651678198", "3168999664907705", "42366404751871660" ]
[ "nonn" ]
49
0
2
null
null
N. J. A. Sloane, Simon Plouffe
2022-06-13T03:03:00
oeisdata/seq/A000/A000660.seq
ad1a40575c8b5a599731d53a55324b92
A000661
Shifts 2 places left under boustrophedon transform.
[ "1", "0", "1", "1", "2", "6", "17", "62", "259", "1230", "6592", "39313", "258575", "1860318", "14538245", "122670593", "1111715644", "10771412394", "111125142979", "1216309735378", "14078811306851", "171837279141312", "2205768169095338", "29707098687614285" ]
[ "nonn", "eigen" ]
24
0
5
null
null
N. J. A. Sloane
2022-02-01T01:09:28
oeisdata/seq/A000/A000661.seq
247e0765a1bf66d16d4d4f5f37c39e1e
A000662
Number of relations with 3 arguments on n nodes.
[ "2", "136", "22377984", "768614354122719232", "354460798875983863749270670915141632", "146267071761884981524915186989628577728537526896649216991428608" ]
[ "nonn", "nice" ]
42
1
1
[ "A000595", "A000662", "A001377", "A051241" ]
[ "M2180", "N0872" ]
N. J. A. Sloane
2024-07-02T15:02:08
oeisdata/seq/A000/A000662.seq
cc88163ed41c3521277d478debf1face
A000663
Number of relations on an infinite set.
[ "1", "2", "9", "37", "183", "933", "5314", "32043", "207212", "1415934", "10200289", "77018442", "607474564", "4987909231", "42519634303", "375395726926" ]
[ "nonn", "nice", "more" ]
25
0
2
null
[ "M1932", "N0763" ]
N. J. A. Sloane
2022-06-17T14:50:49
oeisdata/seq/A000/A000663.seq
dcb47a4df69d7d09ca8df403a6283778
A000664
Number of graphs with n edges.
[ "1", "1", "2", "5", "11", "26", "68", "177", "497", "1476", "4613", "15216", "52944", "193367", "740226", "2960520", "12334829", "53394755", "239544624", "1111261697", "5320103252", "26237509076", "133087001869", "693339241737", "3705135967663", "20286965943329", "113694201046379", "651571521170323", "3815204365835840", "22806847476040913", "139088381010541237", "864777487052916454" ]
[ "nonn", "nice" ]
68
0
3
[ "A000055", "A000088", "A000664", "A002905", "A008406", "A053418", "A275421" ]
[ "M1400", "N0545" ]
N. J. A. Sloane
2025-01-20T12:37:06
oeisdata/seq/A000/A000664.seq
cda5501db30a8f492b4c43017f1939d5
A000665
Number of 3-uniform hypergraphs on n unlabeled nodes, or equivalently number of relations with 3 arguments on n nodes.
[ "1", "1", "1", "2", "5", "34", "2136", "7013320", "1788782616656", "53304527811667897248", "366299663432194332594005123072", "1171638318502989084030402509596875836036608", "3517726593606526072882013063011594224625680712384971214848" ]
[ "nonn", "nice" ]
62
0
4
[ "A000088", "A000665", "A006129", "A038041", "A092337", "A299471", "A301922", "A302374", "A302394", "A306017", "A306021", "A309858", "A320395", "A322451" ]
[ "M1550", "N0606" ]
N. J. A. Sloane
2021-01-08T04:18:59
oeisdata/seq/A000/A000665.seq
6be3b209472321f94aa837638a5328fe
A000666
Number of symmetric relations on n nodes.
[ "1", "2", "6", "20", "90", "544", "5096", "79264", "2208612", "113743760", "10926227136", "1956363435360", "652335084592096", "405402273420996800", "470568642161119963904", "1023063423471189431054720", "4178849203082023236058229792", "32168008290073542372004082199424" ]
[ "nonn", "nice" ]
136
0
2
[ "A000250", "A000595", "A000666", "A001172", "A001174", "A006905", "A054921" ]
[ "M1650", "N0646" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000666.seq
2517f54b65ea3233e0a1f0cdabce9a11
A000667
Boustrophedon transform of all-1's sequence.
[ "1", "2", "4", "9", "24", "77", "294", "1309", "6664", "38177", "243034", "1701909", "13001604", "107601977", "959021574", "9157981309", "93282431344", "1009552482977", "11568619292914", "139931423833509", "1781662223749884", "23819069385695177", "333601191667149054", "4884673638115922509" ]
[ "nonn", "easy", "nice" ]
107
0
2
[ "A000111", "A000667", "A000795", "A002084", "A003719", "A009337", "A009747", "A109449", "A227862", "A292975" ]
null
N. J. A. Sloane and Simon Plouffe
2025-01-05T19:51:31
oeisdata/seq/A000/A000667.seq
8e1a682b776fb1f53d182c114eecfd02
A000668
Mersenne primes (primes of the form 2^n - 1).
[ "3", "7", "31", "127", "8191", "131071", "524287", "2147483647", "2305843009213693951", "618970019642690137449562111", "162259276829213363391578010288127", "170141183460469231731687303715884105727" ]
[ "nonn", "nice", "hard" ]
454
1
1
[ "A000040", "A000043", "A000203", "A000217", "A000225", "A000396", "A000668", "A001348", "A003056", "A007947", "A016027", "A019279", "A023195", "A023758", "A028335", "A034876", "A046051", "A057951", "A057958", "A059305", "A061652", "A083420", "A085104", "A124477", "A135659", "A173898" ]
[ "M2696", "N1080" ]
N. J. A. Sloane
2025-04-03T14:59:41
oeisdata/seq/A000/A000668.seq
e680d1e8babbc7934f72359982392ffe
A000669
Number of series-reduced planted trees with n leaves. Also the number of essentially series series-parallel networks with n edges; also the number of essentially parallel series-parallel networks with n edges.
[ "1", "1", "2", "5", "12", "33", "90", "261", "766", "2312", "7068", "21965", "68954", "218751", "699534", "2253676", "7305788", "23816743", "78023602", "256738751", "848152864", "2811996972", "9353366564", "31204088381", "104384620070", "350064856815", "1176693361956", "3963752002320" ]
[ "nonn", "nice", "easy" ]
157
1
3
[ "A000055", "A000084", "A000311", "A000669", "A001678", "A007827", "A292085", "A292086", "A319254", "A363064" ]
[ "M1421", "N0558" ]
N. J. A. Sloane and John Riordan
2025-02-16T08:32:21
oeisdata/seq/A000/A000669.seq
965141001864586a4105cfb8972c32d2
A000670
Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n].
[ "1", "1", "3", "13", "75", "541", "4683", "47293", "545835", "7087261", "102247563", "1622632573", "28091567595", "526858348381", "10641342970443", "230283190977853", "5315654681981355", "130370767029135901", "3385534663256845323", "92801587319328411133", "2677687796244384203115", "81124824998504073881821" ]
[ "nonn", "core", "nice", "easy" ]
823
0
3
[ "A000629", "A000670", "A002050", "A002144", "A002869", "A004121", "A004122", "A007047", "A007318", "A011782", "A019538", "A032109", "A034172", "A048144", "A052841", "A052856", "A053525", "A074206", "A076726", "A080253", "A080254", "A094416", "A131689", "A135313", "A154921", "A162312", "A163204", "A208744", "A217389", "A226513", "A239914", "A240763", "A242280", "A261781", "A261959", "A262809", "A276890", "A276891", "A290376", "A326322", "A327245", "A327583", "A327584" ]
[ "M2952", "N1191" ]
N. J. A. Sloane
2025-02-20T05:50:34
oeisdata/seq/A000/A000670.seq
69bad1046aecf6b39e0c9935ed6b38ec
A000671
Number of boron trees with n nodes, i.e. n-node rooted trees with degree <= 3 at root and out-degree <= 2 elsewhere.
[ "0", "1", "1", "2", "4", "7", "14", "29", "60", "127", "275", "598", "1320", "2936", "6584", "14858", "33744", "76999", "176557", "406456", "939241", "2177573", "5064150", "11809632", "27610937", "64705623", "151966597", "357623905", "843176524", "1991439229", "4711115672", "11162025770", "26484061667", "62923251955" ]
[ "nonn", "easy", "nice" ]
54
0
4
[ "A000671", "A001190", "A036657", "A036658" ]
[ "M1083", "N0411" ]
N. J. A. Sloane
2023-05-23T21:00:24
oeisdata/seq/A000/A000671.seq
eb4a3a33e08fce392e2ef2c0c2b60c45
A000672
Number of 3-valent trees (= boron trees or binary trees) with n nodes.
[ "1", "1", "1", "1", "2", "2", "4", "6", "11", "18", "37", "66", "135", "265", "552", "1132", "2410", "5098", "11020", "23846", "52233", "114796", "254371", "565734", "1265579", "2841632", "6408674", "14502229", "32935002", "75021750", "171404424", "392658842", "901842517", "2076217086", "4790669518", "11077270335" ]
[ "nonn", "easy", "nice" ]
115
0
5
[ "A000022", "A000200", "A000602", "A000672", "A000673", "A000675", "A001190", "A052120", "A129860", "A144528" ]
[ "M0326", "N0122" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000672.seq
bfbb376b55ab13c5031501432e3b9c9c
A000673
Number of bicentered 3-valent (or boron, or binary) trees with n nodes.
[ "0", "0", "1", "0", "1", "1", "2", "2", "6", "8", "18", "30", "67", "127", "275", "551", "1192", "2507", "5475", "11820", "26007", "57077", "126686", "281625", "630660", "1416116", "3195784", "7232624", "16430563", "37429146", "85528079", "195940960", "450074270", "1036226173", "2391193488", "5529420585" ]
[ "nonn", "easy", "nice" ]
32
0
7
[ "A000022", "A000200", "A000602", "A000672", "A000673", "A000675" ]
[ "M0355", "N0133" ]
N. J. A. Sloane
2020-12-19T03:13:00
oeisdata/seq/A000/A000673.seq
001e806bcb63fb54de96b51859a97f7d
A000674
Boustrophedon transform of 1, 2, 2, 2, 2, ...
[ "1", "3", "7", "16", "43", "138", "527", "2346", "11943", "68418", "435547", "3050026", "23300443", "192835698", "1718682167", "16412205306", "167173350543", "1809239622978", "20732358910387", "250773962554186", "3192953259262243", "42686640718266258", "597853508941160207" ]
[ "nonn" ]
43
0
2
[ "A000111", "A000674", "A040000", "A109449" ]
null
N. J. A. Sloane, Simon Plouffe
2022-06-11T15:55:55
oeisdata/seq/A000/A000674.seq
1f4e9eced72ddd540320a34caa924a5e
A000675
Number of centered 3-valent (or boron, or binary) trees with n nodes.
[ "1", "1", "0", "1", "1", "1", "2", "4", "5", "10", "19", "36", "68", "138", "277", "581", "1218", "2591", "5545", "12026", "26226", "57719", "127685", "284109", "634919", "1425516", "3212890", "7269605", "16504439", "37592604", "85876345", "196717882", "451768247", "1039990913", "2399476030", "5547849750" ]
[ "nonn", "easy", "nice" ]
28
0
7
[ "A000022", "A000200", "A000602", "A000672", "A000673", "A000675" ]
[ "M0977", "N0366" ]
N. J. A. Sloane
2018-09-16T16:58:36
oeisdata/seq/A000/A000675.seq
a42cbd5952e6d386510977bff0103292
A000676
Number of centered trees with n nodes.
[ "1", "1", "0", "1", "1", "2", "3", "7", "12", "27", "55", "127", "284", "682", "1618", "3979", "9823", "24722", "62651", "160744", "415146", "1081107", "2831730", "7462542", "19764010", "52599053", "140580206", "377244482", "1016022191", "2745783463", "7443742141", "20239038700", "55178647926", "150820588425", "413226000775" ]
[ "nonn", "nice", "easy" ]
55
0
6
[ "A000055", "A000081", "A000676", "A000677", "A027416", "A102911" ]
[ "M0831", "N0316" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000676.seq
274614f7f8bd010cfab6c56886c20977
A000677
Number of bicentered trees with n nodes.
[ "0", "0", "1", "0", "1", "1", "3", "4", "11", "20", "51", "108", "267", "619", "1541", "3762", "9497", "23907", "61216", "157211", "407919", "1063398", "2792026", "7365532", "19535887", "52037837", "139213244", "373820978", "1007420841", "2723783122", "7387129661", "20091790330", "54793762295", "149808274055", "410553630946" ]
[ "nonn", "easy", "nice" ]
46
0
7
[ "A000055", "A000676", "A000677" ]
[ "M2366", "N0936" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000677.seq
3d1aa0da7d2a7fb222e4b0e15087d7f1
A000678
Number of carbon (rooted) trees with n carbon atoms = unordered 4-tuples of ternary trees.
[ "0", "1", "1", "2", "4", "9", "18", "42", "96", "229", "549", "1347", "3326", "8330", "21000", "53407", "136639", "351757", "909962", "2365146", "6172068", "16166991", "42488077", "112004630", "296080425", "784688263", "2084521232", "5549613097", "14804572332", "39568107511", "105938822149" ]
[ "nonn", "easy", "nice" ]
37
0
4
null
[ "M1171", "N0448" ]
N. J. A. Sloane, E. M. Rains (rains(AT)caltech.edu)
2018-02-09T21:45:32
oeisdata/seq/A000/A000678.seq
4dd8f3b21ebc60325e96c3a33e824a61
A000679
Number of groups of order 2^n.
[ "1", "1", "2", "5", "14", "51", "267", "2328", "56092", "10494213", "49487367289" ]
[ "nonn", "hard", "more", "nice" ]
90
0
3
[ "A000001", "A000679", "A046058" ]
[ "M1470", "N0581" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000679.seq
9ad84e98dbf103989904430b874a5bbc
A000680
a(n) = (2n)!/2^n.
[ "1", "1", "6", "90", "2520", "113400", "7484400", "681080400", "81729648000", "12504636144000", "2375880867360000", "548828480360160000", "151476660579404160000", "49229914688306352000000", "18608907752179801056000000", "8094874872198213459360000000", "4015057936610313875842560000000" ]
[ "nonn", "easy" ]
192
0
3
[ "A000680", "A001147", "A084939", "A084940", "A084941", "A084942", "A084943", "A084944", "A087127", "A089759", "A097591", "A132101", "A187783", "A241171", "A267479", "A267480" ]
[ "M4287", "N1793" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000680.seq
4580957d1925fd39d0ff0152b1a29ab5
A000681
Number of n X n matrices with nonnegative entries and every row and column sum 2.
[ "1", "1", "3", "21", "282", "6210", "202410", "9135630", "545007960", "41514583320", "3930730108200", "452785322266200", "62347376347779600", "10112899541133589200", "1908371363842760216400", "414517594539154672566000", "102681435747106627787376000", "28772944645196614863048048000" ]
[ "nonn", "nice", "easy" ]
119
0
3
[ "A000142", "A000681", "A001499", "A001500", "A005650", "A123544", "A172806", "A172862", "A172894", "A172919", "A172944", "A172958", "A257493", "A269742", "A307804" ]
[ "M3084", "N1250" ]
N. J. A. Sloane, Simon Plouffe
2023-10-27T18:25:44
oeisdata/seq/A000/A000681.seq
6a2b108c783d2b3f569227637b207275
A000682
Semi-meanders: number of ways a semi-infinite directed curve can cross a straight line n times.
[ "1", "1", "2", "4", "10", "24", "66", "174", "504", "1406", "4210", "12198", "37378", "111278", "346846", "1053874", "3328188", "10274466", "32786630", "102511418", "329903058", "1042277722", "3377919260", "10765024432", "35095839848", "112670468128", "369192702554", "1192724674590", "3925446804750" ]
[ "nonn", "nice" ]
204
1
3
[ "A000136", "A000560", "A000682", "A001011", "A001997", "A086441", "A259689" ]
[ "M1205", "N0464" ]
N. J. A. Sloane
2024-11-18T22:31:33
oeisdata/seq/A000/A000682.seq
3899534b28af934ada1b9520c71439a6
A000683
Number of colorings of labeled graphs on n nodes using exactly 2 colors, divided by 4.
[ "0", "1", "6", "40", "360", "4576", "82656", "2122240", "77366400", "4002843136", "293717546496", "30558458490880", "4505780560619520", "941417163728674816", "278628902101315608576", "116805328001281573519360" ]
[ "nonn", "nice", "easy" ]
37
1
3
[ "A000683", "A047863", "A058843", "A213441" ]
[ "M4238", "N1770" ]
N. J. A. Sloane
2015-11-25T01:40:11
oeisdata/seq/A000/A000683.seq
b11bc5e5dcc500b88da4a21ddb83810c
A000684
Number of colored labeled n-node graphs with 2 interchangeable colors.
[ "1", "3", "13", "81", "721", "9153", "165313", "4244481", "154732801", "8005686273", "587435092993", "61116916981761", "9011561121239041", "1882834327457349633", "557257804202631217153", "233610656002563147038721", "138681207656726645785559041" ]
[ "nonn", "nice", "easy" ]
73
1
2
[ "A000683", "A000684", "A058872", "A111636", "A134531" ]
[ "M2954", "N1192" ]
N. J. A. Sloane
2023-10-27T18:25:40
oeisdata/seq/A000/A000684.seq
78d378572d4d47be50e7e36740a25bde
A000685
Number of 3-colored labeled graphs on n nodes, divided by 3.
[ "1", "5", "41", "545", "11681", "402305", "22207361", "1961396225", "276825510401", "62368881977345", "22413909724518401", "12840603873823473665", "11720394922432296755201", "17037597932370037286600705" ]
[ "nonn", "easy", "nice" ]
39
1
2
[ "A000683", "A000685", "A047863", "A191371", "A223887" ]
[ "M3995", "N1656" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000685.seq
0b1a7773e4a7b3b8dbe91f0738118113
A000686
Number of 4-colored labeled graphs on n nodes, divided by 4.
[ "1", "7", "85", "1777", "63601", "3882817", "403308865", "71139019777", "21276992674561", "10778161937857537", "9238819435213784065", "13390649605615389843457", "32796747486424209782108161", "135669064080920007649863745537", "947468281528010179181982467702785", "11166618111585805201637975219611631617" ]
[ "nonn", "easy", "nice" ]
49
1
2
[ "A000683", "A000685", "A000686", "A223887" ]
[ "M4449", "N1884" ]
N. J. A. Sloane
2023-09-13T04:43:28
oeisdata/seq/A000/A000686.seq
4d6733aaba32300f22c739043e0809b8
A000687
Boustrophedon transform (first version) of Fibonacci numbers 0,1,1,2,3,5,...
[ "1", "1", "2", "6", "17", "59", "229", "1029", "5242", "30040", "191201", "1338897", "10228097", "84647981", "754437958", "7204350870", "73382899597", "794189092567", "9100736472725", "110080467183393", "1401588037032782", "18737851806495008", "262435512896178877" ]
[ "nonn" ]
42
0
3
[ "A000045", "A000687", "A000738", "A000744", "A092073" ]
null
N. J. A. Sloane and Simon Plouffe
2024-05-04T05:31:52
oeisdata/seq/A000/A000687.seq
8289f92911b1f89a77d2f035d91c981a
A000688
Number of Abelian groups of order n; number of factorizations of n into prime powers.
[ "1", "1", "1", "2", "1", "1", "1", "3", "2", "1", "1", "2", "1", "1", "1", "5", "1", "2", "1", "2", "1", "1", "1", "3", "2", "1", "3", "2", "1", "1", "1", "7", "1", "1", "1", "4", "1", "1", "1", "3", "1", "1", "1", "2", "2", "1", "1", "5", "2", "2", "1", "2", "1", "3", "1", "3", "1", "1", "1", "2", "1", "1", "2", "11", "1", "1", "1", "2", "1", "1", "1", "6", "1", "1", "2", "2", "1", "1", "1", "5", "5", "1", "1", "2", "1", "1", "1", "3", "1", "2", "1", "2", "1", "1", "1", "7", "1", "2", "2", "4", "1", "1", "1", "3", "1", "1", "1" ]
[ "nonn", "core", "easy", "nice", "mult" ]
195
1
4
[ "A000001", "A000041", "A000688", "A000961", "A001055", "A005361", "A021002", "A034382", "A046054", "A046055", "A046056", "A046101", "A050360", "A050361", "A051532", "A055653", "A057521", "A060689", "A080729", "A101872", "A101876", "A124010", "A129667", "A369634" ]
[ "M0064", "N0020" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000688.seq
e1124d7a0a3514a38ce76332e4d00baf
A000689
Final decimal digit of 2^n.
[ "1", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6", "2", "4", "8", "6" ]
[ "nonn", "base", "easy" ]
84
0
2
[ "A000079", "A000689", "A000855", "A008952", "A034887", "A173635" ]
null
N. J. A. Sloane
2024-07-06T21:09:28
oeisdata/seq/A000/A000689.seq
98df8816e2e5990b6c1058fc1dc2fb9b
A000690
Landau's approximation to population of x^2 + y^2 <= 2^n.
[ "1", "2", "3", "4", "7", "13", "24", "44", "83", "157", "297", "567", "1085", "2086", "4019", "7766", "15039", "29181", "56717", "110408", "215225", "420076", "820836", "1605587", "3143562", "6160098", "12080946", "23710229", "46565965", "91512121", "179947985", "354043613", "696935548", "1372589372" ]
[ "nonn" ]
32
0
2
[ "A000050", "A000690", "A064533" ]
[ "M0586", "N0212" ]
N. J. A. Sloane
2022-05-13T18:49:36
oeisdata/seq/A000/A000690.seq
2fef4c1c29eec5093ebda18c65356884
A000691
Ramanujan's approximation to population of x^2 + y^2 <= 2^n.
[ "1", "2", "3", "5", "9", "16", "29", "52", "94", "175", "327", "616", "1169", "2231", "4273", "8215", "15842", "30628", "59345", "115208", "224040", "436343", "850981", "1661663", "3248231", "6356076", "12448925", "24402959", "47873156", "93984236", "184632691", "362938014", "713852252", "1404817026" ]
[ "nonn" ]
35
0
2
[ "A000050", "A000690", "A000691", "A000692", "A064533" ]
[ "M0713", "N0263" ]
N. J. A. Sloane
2022-05-23T09:11:53
oeisdata/seq/A000/A000691.seq
f4aa0efbc5cf41c07205251c55f7a846
A000692
An approximation to population of x^2 + y^2 <= 2^n.
[ "1", "3", "4", "5", "9", "15", "27", "50", "92", "171", "322", "610", "1161", "2220", "4260", "8201", "15828", "30622", "59362", "115287", "224260", "436871", "852161", "1664196", "3253531", "6366973", "12471056", "24447507", "47962236", "94161474", "184983976", "363632192", "715220838", "1407510311" ]
[ "nonn" ]
40
0
2
[ "A000050", "A000690", "A000691", "A000692", "A064533" ]
[ "M2311", "N0913" ]
N. J. A. Sloane
2023-08-06T23:33:59
oeisdata/seq/A000/A000692.seq
452ab50dfceeffe1c100c8e7423612e0
A000693
Related to population of numbers of form x^2 + y^2.
[ "1", "2", "3", "6", "10", "19", "35", "62", "118", "219", "414", "783", "1497", "2860", "5503", "10593", "20471", "39637", "76918", "149501", "291115", "567581", "1108022", "2165621", "4237085", "8297727", "16264207", "31904254", "62630372", "123031586", "241837446", "475647114", "936020000", "1842925873" ]
[ "nonn" ]
21
1
2
null
[ "M0767", "N0292" ]
N. J. A. Sloane
2022-02-01T01:09:59
oeisdata/seq/A000/A000693.seq
248c6480f647e6a7b56c02f8566c2522
A000694
Related to population of numbers of form x^2 + y^2.
[ "1", "2", "4", "6", "11", "19", "34", "63", "117", "218", "411", "780", "1487", "2849", "5477", "10562", "20419", "39563", "76805", "149360", "290896", "567321", "1107775", "2165487", "4237384", "8299283", "16268639", "31915437", "62656158", "123088460", "241958676", "475901501", "936544684" ]
[ "nonn" ]
22
1
2
[ "A000691", "A000694" ]
[ "M1021", "N0384" ]
N. J. A. Sloane
2014-03-15T05:14:52
oeisdata/seq/A000/A000694.seq
0d4d966c7f5e8c0702039095eba95b85
A000695
Moser-de Bruijn sequence: sums of distinct powers of 4.
[ "0", "1", "4", "5", "16", "17", "20", "21", "64", "65", "68", "69", "80", "81", "84", "85", "256", "257", "260", "261", "272", "273", "276", "277", "320", "321", "324", "325", "336", "337", "340", "341", "1024", "1025", "1028", "1029", "1040", "1041", "1044", "1045", "1088", "1089", "1092", "1093", "1104", "1105", "1108", "1109", "1280", "1281", "1284", "1285" ]
[ "nonn", "nice", "easy" ]
302
0
3
[ "A000012", "A000027", "A000225", "A000302", "A000695", "A001196", "A001316", "A001511", "A005836", "A007088", "A007583", "A033042", "A033052", "A039966", "A048720", "A048723", "A048883", "A059884", "A059901", "A059904", "A059905", "A059906", "A062880", "A102376", "A104257", "A117940", "A126684", "A145812", "A151665", "A151666", "A151667", "A151668", "A151669", "A151670", "A151671", "A151672", "A151673", "A151674" ]
[ "M3259", "N1315" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000695.seq
7d3fbeeeac8c39822d3866819d428822
A000696
Numbers k such that (1,k) is "good".
[ "1", "7", "31", "37", "109", "121", "127", "133", "151", "157", "403", "421", "511", "529", "631", "637", "661", "679", "1579", "1621", "1633", "1969", "1981", "2017", "2041", "2047", "2053", "2071", "2077", "2143", "2149", "2167", "2173", "2401", "2527", "2557", "2677", "6493", "6559", "6643", "6661", "6703", "6733", "6871" ]
[ "nonn", "base" ]
25
1
2
[ "A000695", "A000696" ]
[ "M4397", "N1853" ]
N. J. A. Sloane
2022-02-02T03:57:58
oeisdata/seq/A000/A000696.seq
8a131e81ffa71ca89b241b8eae42a052
A000697
Boustrophedon transform of 1, 1, 4, 9, 16, ...
[ "1", "2", "7", "26", "89", "316", "1243", "5564", "28321", "162160", "1032051", "7226636", "55206161", "456886912", "4072080587", "38885496092", "396084390849", "4286637591872", "49121248360291", "594159600856332", "7565074996215025", "101137602761945440" ]
[ "nonn" ]
51
0
2
[ "A000290", "A000697", "A000745", "A109449" ]
null
N. J. A. Sloane, Simon Plouffe
2022-06-12T12:00:51
oeisdata/seq/A000/A000697.seq
22680b25e13fd2274a07649b56d0fa81
A000698
A problem of configurations: a(0) = 1; for n>0, a(n) = (2n-1)!! - Sum_{k=1..n-1} (2k-1)!! a(n-k). Also the number of shellings of an n-cube, divided by 2^n n!.
[ "1", "1", "2", "10", "74", "706", "8162", "110410", "1708394", "29752066", "576037442", "12277827850", "285764591114", "7213364729026", "196316804255522", "5731249477826890", "178676789473121834", "5925085744543837186", "208256802758892355202", "7734158085942678174730" ]
[ "nonn", "easy", "nice" ]
282
0
3
[ "A000165", "A000168", "A000260", "A000309", "A000698", "A000699", "A001147", "A002005", "A004208", "A005411", "A005412", "A053979", "A062980", "A115974", "A167872", "A258219", "A258222", "A267827", "A322398" ]
[ "M1974", "N0783" ]
N. J. A. Sloane, Richard Ehrenborg, Gabor Hetyei
2025-02-01T23:16:24
oeisdata/seq/A000/A000698.seq
136a62b5eb98442b56c5256adbcd7ac4
A000699
Number of irreducible chord diagrams with 2n nodes.
[ "1", "1", "1", "4", "27", "248", "2830", "38232", "593859", "10401712", "202601898", "4342263000", "101551822350", "2573779506192", "70282204726396", "2057490936366320", "64291032462761955", "2136017303903513184", "75197869250518812754", "2796475872605709079512", "109549714522464120960474", "4509302910783496963256400", "194584224274515194731540740" ]
[ "nonn", "easy", "nice" ]
228
0
4
[ "A000168", "A000260", "A000309", "A000698", "A000699", "A002005", "A004300", "A007297", "A016098", "A051862", "A062980", "A099947", "A136653", "A212273", "A232223", "A267827", "A268815", "A306438", "A322402", "A324166", "A324172", "A324173", "A324327" ]
[ "M3618", "N1468" ]
N. J. A. Sloane
2025-03-28T10:11:07
oeisdata/seq/A000/A000699.seq
0ebb7168aa3159997030c50b4607f09b
A000700
Expansion of Product_{k>=0} (1 + x^(2k+1)); number of partitions of n into distinct odd parts; number of self-conjugate partitions; number of symmetric Ferrers graphs with n nodes.
[ "1", "1", "0", "1", "1", "1", "1", "1", "2", "2", "2", "2", "3", "3", "3", "4", "5", "5", "5", "6", "7", "8", "8", "9", "11", "12", "12", "14", "16", "17", "18", "20", "23", "25", "26", "29", "33", "35", "37", "41", "46", "49", "52", "57", "63", "68", "72", "78", "87", "93", "98", "107", "117", "125", "133", "144", "157", "168", "178", "192", "209", "223", "236", "255", "276", "294", "312", "335", "361", "385" ]
[ "nonn", "easy", "nice" ]
293
0
9
[ "A000009", "A000041", "A000700", "A000701", "A046682", "A052002", "A053250", "A069910", "A069911", "A081362", "A085547", "A088994", "A146061", "A169987", "A169995", "A218907", "A295291", "A304044" ]
[ "M0217", "N0078" ]
N. J. A. Sloane
2025-02-16T08:32:21
oeisdata/seq/A000/A000700.seq
62dfe5a75630b3de0a9c07f1365d044e