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oeis

Dataset card Data Studio Files
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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
A006701
Exponentiation of g.f. for Fibonacci numbers.
[ "0", "1", "1", "5", "13", "60", "246", "1266", "6679", "39568", "247940", "1677435", "12020295", "91463410", "733490265", "6189608760", "54746987035", "506444804075", "4887127598817", "49096724251235", "512474550910080", "5548429401985372", "62208756548406172", "721256031012180537", "8635815672831322186" ]
[ "nonn" ]
16
0
4
[ "A000045", "A006701", "A007552", "A256180" ]
null
N. J. A. Sloane.
2021-06-08T08:48:32
oeisdata/seq/A006/A006701.seq
942a94ea9d10bb0c247cce1b83f682dc
A006702
Solution to a Pellian equation: least x such that x^2 - n*y^2 = +- 1.
[ "1", "1", "2", "1", "2", "5", "8", "3", "1", "3", "10", "7", "18", "15", "4", "1", "4", "17", "170", "9", "55", "197", "24", "5", "1", "5", "26", "127", "70", "11", "1520", "17", "23", "35", "6", "1", "6", "37", "25", "19", "32", "13", "3482", "199", "161", "24335", "48", "7", "1", "7", "50", "649", "182", "485", "89", "15", "151", "99", "530", "31", "29718", "63", "8", "1", "8", "65", "48842" ]
[ "nonn", "nice", "easy" ]
53
1
3
[ "A006702", "A006703", "A077232" ]
[ "M0120" ]
N. J. A. Sloane
2021-12-22T00:05:17
oeisdata/seq/A006/A006702.seq
57dfe904c43a87e5b3c5ba9e58d7cdc9
A006703
Solution to Pellian: y such that x^2 - n*y^2 = +-1.
[ "0", "1", "1", "0", "1", "2", "3", "1", "0", "1", "3", "2", "5", "4", "1", "0", "1", "4", "39", "2", "12", "42", "5", "1", "0", "1", "5", "24", "13", "2", "273", "3", "4", "6", "1", "0", "1", "6", "4", "3", "5", "2", "531", "30", "24", "3588", "7", "1", "0", "1", "7", "90", "25", "66", "12", "2", "20", "13", "69", "4", "3805", "8", "1", "0", "1", "8", "5967", "4", "936", "30", "413", "2", "125", "5", "3", "6630", "40", "6", "9" ]
[ "nonn" ]
37
1
6
[ "A006702", "A006703", "A077233" ]
[ "M0399" ]
N. J. A. Sloane
2021-12-26T21:50:33
oeisdata/seq/A006/A006703.seq
9f025c36c1f5174f1e8c578aab424256
A006704
Solution to Pellian: x such that x^2 - n y^2 = +- 1, +- 4.
[ "1", "1", "2", "1", "1", "5", "8", "2", "1", "3", "10", "4", "3", "15", "4", "1", "4", "17", "170", "4", "5", "197", "24", "5", "1", "5", "26", "16", "5", "11", "1520", "6", "23", "35", "6", "1", "6", "37", "25", "6", "32", "13", "3482", "20", "7", "24335", "48", "7", "1", "7", "50", "36", "7", "485", "89", "15", "151", "99", "530", "8", "39", "63", "8", "1", "8", "65", "48842", "8", "25", "251", "3480", "17", "1068", "43" ]
[ "nonn" ]
27
1
3
[ "A006704", "A006705" ]
[ "M0119" ]
N. J. A. Sloane.
2017-10-18T02:47:10
oeisdata/seq/A006/A006704.seq
ba8abd62893317b9425b25c154986379
A006705
Solution to Pellian: y such that x^2 - n y^2 = +- 1, +- 4.
[ "0", "1", "1", "0", "1", "2", "3", "1", "0", "1", "3", "1", "1", "4", "1", "0", "1", "4", "39", "1", "1", "42", "5", "1", "0", "1", "5", "3", "1", "2", "273", "1", "4", "6", "1", "0", "1", "6", "4", "1", "5", "2", "531", "3", "1", "3588", "7", "1", "0", "1", "7", "5", "1", "66", "12", "2", "20", "13", "69", "1", "5", "8", "1", "0", "1", "8", "5967", "1", "3", "30", "413", "2", "125", "5", "3", "39", "1", "6", "9", "1", "0", "1", "9", "6", "1", "1122", "3", "21", "53" ]
[ "nonn", "easy", "nice" ]
32
1
6
[ "A006704", "A006705" ]
[ "M0398" ]
N. J. A. Sloane
2023-10-29T21:17:50
oeisdata/seq/A006/A006705.seq
ed054401148455dda4becdf61b531fb0
A006706
Self-convolution of numbers of trees on n nodes.
[ "1", "2", "3", "4", "7", "12", "23", "44", "90", "186", "407", "902", "2072", "4844", "11595", "28150", "69491", "173522", "438423", "1117968", "2875960", "7453070", "19447591", "51050224", "134749849", "357446716", "952527403", "2548897192", "6846986075", "18458150242", "49923931099", "135443922536", "368511905808" ]
[ "nonn" ]
28
0
2
[ "A000055", "A006706" ]
null
N. J. A. Sloane.
2016-10-04T15:44:55
oeisdata/seq/A006/A006706.seq
a0b39653cc1302ea836ed00319fd02b2
A006707
Expansion of a modular function.
[ "1", "7", "24", "50", "58", "3", "-120", "-200", "-39", "402", "728", "246", "-1200", "-2338", "-1032", "3188", "6654", "3357", "-7880", "-17300", "-9354", "18680", "42224", "23748", "-42590", "-98109", "-56568", "93214", "218068", "127821", "-197056", "-465888", "-275949", "405044", "962936", "573660", "-811156", "-1934558", "-1155768", "1584700", "3787096" ]
[ "sign", "easy" ]
13
-2
2
null
[ "M4383" ]
N. J. A. Sloane
2021-12-26T21:50:43
oeisdata/seq/A006/A006707.seq
22651dd221c09b891d6a1f4f2cf96460
A006708
Expansion of a modular function for gamma_0(6).
[ "1", "-1", "-8", "2", "26", "27", "-24", "-136", "-135", "162", "568", "486", "-624", "-1970", "-1512", "1940", "5886", "4293", "-5480", "-15796", "-11178", "14264", "39472", "27108", "-34526", "-93285", "-62424", "79054", "209684", "137781", "-173248", "-451680", "-292653", "365780", "939736", "601020", "-747220", "-1897294", "-1199448", "1482652", "3727832" ]
[ "sign", "easy" ]
13
-2
3
null
[ "M4469" ]
N. J. A. Sloane
2021-12-26T21:50:51
oeisdata/seq/A006/A006708.seq
83e8a77798d7e28150c2d581749a9bc8
A006709
Expansion of a modular function.
[ "1", "-2", "-3", "-4", "22", "30", "-12", "-128", "-147", "132", "548", "516", "-552", "-1924", "-1572", "1784", "5790", "4410", "-5180", "-15608", "-11406", "13712", "39128", "27528", "-33518", "-92682", "-63156", "77284", "208636", "139026", "-170272", "-449904", "-294741", "360872", "936836", "604440", "-739228", "-1892636" ]
[ "sign", "easy" ]
28
-2
2
null
[ "M0600" ]
N. J. A. Sloane
2018-04-03T03:34:34
oeisdata/seq/A006/A006709.seq
6995fa9e31e1021e9302c02ef5e3d2dc
A006710
Expansion of eta(q^10)^12/(eta(q^2)^4*eta(q^5)^8) in powers of q.
[ "1", "0", "4", "0", "14", "8", "40", "32", "105", "112", "284", "320", "702", "840", "1688", "2112", "3860", "4976", "8540", "11264", "18424", "24480", "38584", "51520", "78901", "105648", "157600", "211136", "308310", "412872", "592224", "791040", "1117441", "1488160", "2074924", "2754048", "3794660", "5018408" ]
[ "nonn", "easy" ]
20
3
3
null
[ "M3190" ]
N. J. A. Sloane
2015-11-25T12:18:28
oeisdata/seq/A006/A006710.seq
3eb760946f66baf3b85749fda8649a9d
A006711
Describe previous term from the right (method A - initial term is 1).
[ "1", "11", "21", "1112", "1231", "11131211", "2112111331", "112331122112", "12212221231221", "11221113121132112211", "212221121321121113312221", "113211233112211213111221321112" ]
[ "nonn", "base", "easy", "nice" ]
25
1
2
[ "A005150", "A006711", "A022482", "A022506", "A022507", "A022513" ]
[ "M4778" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006711.seq
14fe1cd1e636989d3d1690a950bc1457
A006712
Number of 3-edge-colored trivalent graphs with 2n labeled nodes.
[ "6", "480", "197820", "150474240", "208857587400", "471804812519040", "1625459273858019600", "8112729590064978278400", "56342429224416522460072800", "527075322501595757416502976000", "6466573585901882433727764077860800", "101749747195531624711768653503416320000" ]
[ "nonn" ]
25
2
1
[ "A002830", "A002831", "A005638", "A006712", "A006713", "A248361" ]
[ "M4311" ]
N. J. A. Sloane
2017-12-18T22:44:55
oeisdata/seq/A006/A006712.seq
b64a9414d47ee81b79263d354b06afe2
A006713
Number of 3-edge-colored connected trivalent graphs with 2n labeled nodes.
[ "6", "480", "196560", "149869440", "208166112000", "470619551001600", "1622357050938624000", "8100931274981056512000", "56279222605087617687552000", "526611567858781597240688640000", "6462027944190599588931310387200000", "101691538301880025620001692844032000000" ]
[ "nonn" ]
19
2
1
[ "A002830", "A002831", "A002851", "A006712", "A006713", "A248362" ]
[ "M4310" ]
N. J. A. Sloane
2017-12-18T22:45:05
oeisdata/seq/A006/A006713.seq
966137b37349029175a218d761766e6f
A006714
Number of trivalent bipartite labeled graphs with 2n labeled nodes.
[ "10", "840", "257040", "137260200", "118273755600", "154712104747200", "292311804557572800", "766931112143320924800", "2706462791802644002128000", "12512595130808078973370704000", "74130965352250071944327288640000", "552334353713465817349513210512960000", "5092566798555894395129552704613028960000" ]
[ "nonn" ]
26
3
1
[ "A001501", "A002829", "A004109", "A006714", "A246599" ]
[ "M4757" ]
N. J. A. Sloane
2024-02-17T05:45:49
oeisdata/seq/A006/A006714.seq
6ce545da8009e62118b3979bd0f09389
A006715
Describe the previous term! (method A - initial term is 3).
[ "3", "13", "1113", "3113", "132113", "1113122113", "311311222113", "13211321322113", "1113122113121113222113", "31131122211311123113322113", "132113213221133112132123222113", "11131221131211132221232112111312111213322113", "31131122211311123113321112131221123113111231121123222113" ]
[ "nonn", "base", "easy", "nice" ]
52
1
1
[ "A001140", "A001141", "A001143", "A001145", "A001151", "A001154", "A001155", "A005150", "A006715", "A006751", "A088204" ]
[ "M2965" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006715.seq
eb270a1b267ef0d0376808e8e4fd1a6d
A006716
Squares with digits 1, 4, 9.
[ "1", "4", "9", "49", "144", "441", "1444", "11449", "44944", "991494144", "4914991449", "149991994944", "9141411499911441", "199499144494999441", "9914419419914449449", "444411911999914911441", "419994999149149944149149944191494441" ]
[ "nonn", "base" ]
33
1
2
[ "A006716", "A019544", "A027675", "A053059", "A058411", "A058472", "A058473", "A058474", "A061269" ]
[ "M3369" ]
N. J. A. Sloane, revised Jul 10 2015
2025-03-25T15:31:04
oeisdata/seq/A006/A006716.seq
b32e5e7742eb2e8bbd482cd404368011
A006717
Number of ways of arranging 2n+1 nonattacking semi-queens on a (2n+1) X (2n+1) toroidal board.
[ "1", "3", "15", "133", "2025", "37851", "1030367", "36362925", "1606008513", "87656896891", "5778121715415", "452794797220965", "41609568918940625" ]
[ "nonn", "more", "nice" ]
100
0
2
[ "A003111", "A006717", "A007705" ]
[ "M3005" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006717.seq
9dfb96b6e27ec75e9f7dcb642b4d5bc8
A006718
Number of golygons of length 8n.
[ "1", "4", "112", "8432", "909288", "121106960", "18167084064", "2956370702688", "510696155882492", "92343039606440064", "17311893232788414400", "3342127071364266721200", "661066887819006986788620", "133456726466163517072371360" ]
[ "nonn" ]
42
0
2
[ "A006718", "A007219", "A060468", "A063865", "A292476" ]
[ "M3707" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006718.seq
9a471c4d5b0804746e89a9534bdd04c9
A006719
a(n) = A000905(n) + 1.
[ "3", "4", "6", "12", "48", "924", "409620", "83763206256", "3508125906290858798172", "6153473687096578758448522809275077520433168", "18932619208894981833333582059033329370801266249535902023330546944758507753065602135844" ]
[ "nonn" ]
11
1
1
null
[ "M2328" ]
N. J. A. Sloane.
2013-06-11T16:32:37
oeisdata/seq/A006/A006719.seq
b0a6328293fa7e090b343b24021dec8c
A006720
Somos-4 sequence: a(0)=a(1)=a(2)=a(3)=1; for n >= 4, a(n) = (a(n-1) * a(n-3) + a(n-2)^2) / a(n-4).
[ "1", "1", "1", "1", "2", "3", "7", "23", "59", "314", "1529", "8209", "83313", "620297", "7869898", "126742987", "1687054711", "47301104551", "1123424582771", "32606721084786", "1662315215971057", "61958046554226593", "4257998884448335457", "334806306946199122193", "23385756731869683322514", "3416372868727801226636179" ]
[ "nonn", "easy", "nice" ]
237
0
5
[ "A006720", "A006721", "A006722", "A006723", "A006769", "A028935", "A028945", "A048736", "A051138", "A129739", "A129740", "A129741", "A151502", "A165896", "A178384", "A188313", "A227199", "A247368" ]
[ "M0857" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006720.seq
69a7caf3945e179efb9bde4e37e859b7
A006721
Somos-5 sequence: a(n) = (a(n-1) * a(n-4) + a(n-2) * a(n-3)) / a(n-5), with a(0) = a(1) = a(2) = a(3) = a(4) = 1.
[ "1", "1", "1", "1", "1", "2", "3", "5", "11", "37", "83", "274", "1217", "6161", "22833", "165713", "1249441", "9434290", "68570323", "1013908933", "11548470571", "142844426789", "2279343327171", "57760865728994", "979023970244321", "23510036246274433", "771025645214210753" ]
[ "easy", "nonn", "nice" ]
163
0
6
[ "A006720", "A006721", "A006722", "A006723", "A048736" ]
[ "M0735" ]
N. J. A. Sloane
2025-02-17T14:40:40
oeisdata/seq/A006/A006721.seq
02b3ba21a44e2c28d4ec5a814141a2ed
A006722
Somos-6 sequence: a(n) = (a(n-1) * a(n-5) + a(n-2) * a(n-4) + a(n-3)^2) / a(n-6), a(0) = ... = a(5) = 1.
[ "1", "1", "1", "1", "1", "1", "3", "5", "9", "23", "75", "421", "1103", "5047", "41783", "281527", "2534423", "14161887", "232663909", "3988834875", "45788778247", "805144998681", "14980361322965", "620933643034787", "16379818848380849", "369622905371172929", "20278641689337631649", "995586066665500470689" ]
[ "nonn", "easy", "nice" ]
99
0
7
[ "A006720", "A006721", "A006722", "A006723", "A048736" ]
[ "M2457" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006722.seq
b5493a6185f491f2a7bae88db3f0e425
A006723
Somos-7 sequence: a(n) = (a(n-1) * a(n-6) + a(n-2) * a(n-5) + a(n-3) * a(n-4)) / a(n-7), a(0) = ... = a(6) = 1.
[ "1", "1", "1", "1", "1", "1", "1", "3", "5", "9", "17", "41", "137", "769", "1925", "7203", "34081", "227321", "1737001", "14736001", "63232441", "702617001", "8873580481", "122337693603", "1705473647525", "22511386506929", "251582370867257", "9254211194697641", "215321535159114017" ]
[ "nonn", "easy", "nice" ]
85
0
8
[ "A006720", "A006721", "A006722", "A006723", "A048736", "A078495" ]
[ "M2456" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006723.seq
bae292af66c4c39d7075ffe6ae561b37
A006724
Number of fixed n-celled self-avoiding polygons on square lattice.
[ "1", "2", "6", "19", "63", "216", "756", "2684", "9638", "34930", "127560", "468837", "1732702", "6434322", "23993874", "89805691", "337237337", "1270123530", "4796310672", "18155586993", "68874803609", "261803388854", "996971935098", "3802944302442", "14528816598358" ]
[ "nonn", "nice" ]
32
1
2
[ "A002931", "A006724" ]
[ "M1637" ]
N. J. A. Sloane, Simon Plouffe
2024-09-04T12:02:45
oeisdata/seq/A006/A006724.seq
afe9e85cd70b3b15ab11d1cf0cef3cf7
A006725
Number of n-celled polygons with perimeter 2n+2 on square lattice.
[ "1", "2", "6", "18", "55", "174", "566", "1868", "6237", "21050", "71666", "245696", "847317", "2937116", "10226574", "35746292", "125380257", "441125966", "1556301578", "18155586993" ]
[ "nonn" ]
16
1
2
null
[ "M1623" ]
N. J. A. Sloane, Simon Plouffe
2012-03-31T10:23:10
oeisdata/seq/A006/A006725.seq
d53e9e82de27f83568f17c5f43918ac4
A006726
Number of n-celled polygons with perimeter 2n on square lattice.
[ "1", "8", "40", "168", "676", "2672", "10376", "39824", "151878", "576656", "2181496", "8229160", "30974700", "116385088", "436678520", "1636472360", "6126647748" ]
[ "nonn" ]
15
4
2
null
[ "M4523" ]
N. J. A. Sloane, Simon Plouffe
2015-07-07T17:42:48
oeisdata/seq/A006/A006726.seq
fbd7373f7ff8477dc8f9c75236a35bf7
A006727
Bond percolation series for square lattice.
[ "1", "2", "4", "8", "15", "28", "50", "90", "156", "274", "466", "804", "1348", "2300", "3804", "6450", "10547", "17784", "28826", "48464", "77689", "130868", "207308", "350014", "548271", "931584", "1433966", "2469368", "3725257", "6510384", "9590838", "17192714", "24357702", "45428434", "61388268", "119938514", "152169019", "320596894", "366032458", "863591282", "863729021", "2341276788", "1916799026", "6556348906", "3755360368", "18610776960", "6082131438", "53874179752", "1495903344", "164440159702", "-48816119038", "507516102724", "-288652716240", "1605880660392", "-1407950918758" ]
[ "sign", "nice" ]
23
0
2
null
[ "M1105" ]
N. J. A. Sloane, Simon Plouffe
2019-01-08T03:05:17
oeisdata/seq/A006/A006727.seq
7fe6f58fca5cf5429640948758591e73
A006728
Series for first parallel moment of square lattice.
[ "2", "8", "24", "62", "148", "330", "710", "1464", "2962", "5814", "11288", "21406", "40364", "74570", "137602", "249088", "451868", "804766", "1440580", "2529686", "4482584", "7775166", "13664146", "23446020", "40953840", "69518842", "120978656", "203223692", "352808860", "586473542", "1018405966", "1671890010", "2913173846", "4717224772", "8265261498", "13170191912", "23329646078", "36355510686", "65539706454", "99432015478", "183391807808", "268568296956", "513870876498", "714234719598", "1440359201368", "1874047502574", "4048390833688", "4791576314698", "11521319804730", "11801670105578", "33055165149064", "27869200356228", "96170461301080", "58847785748014", "288365269158218", "97008272891722", "876853221827434", "50270991328638", "2742424862540904", "-723012645772984", "8945610206297122" ]
[ "sign", "nice" ]
19
0
1
[ "A006727", "A006728", "A006729", "A006730", "A260330" ]
[ "M1840" ]
N. J. A. Sloane, Simon Plouffe
2019-10-04T07:39:10
oeisdata/seq/A006/A006728.seq
a8f4067ab8db2c4c8caa913d224d5318
A006729
Series for second parallel moment of square lattice (eventually changes sign).
[ "2", "16", "72", "252", "764", "2094", "5362", "12968", "30138", "67446", "147048", "311940", "649860", "1325234", "2668130", "5278066", "10346200", "19977010", "38329556", "72546986", "136785444", "254596418", "473093498", "868060738", "1593517724" ]
[ "sign" ]
25
0
1
[ "A006461", "A006727", "A006728", "A006729", "A006730", "A260330" ]
[ "M2088" ]
N. J. A. Sloane, Simon Plouffe
2019-10-05T09:15:12
oeisdata/seq/A006/A006729.seq
6fd777929ea8284f0e31cd3718489968
A006730
Series for second perpendicular moment of square lattice (eventually changes sign).
[ "0", "2", "8", "24", "64", "156", "358", "786", "1664", "3434", "6902", "13656", "26464", "50772", "95754", "179442", "331294", "609496", "1106106", "2004852", "3586874", "6423028", "11351274", "20126538", "35191190", "61883196", "107179834", "187216848", "321395596", "558468104" ]
[ "sign" ]
20
0
2
[ "A006461", "A006727", "A006728", "A006729", "A006730" ]
[ "M1841" ]
N. J. A. Sloane, Simon Plouffe
2015-09-19T09:24:53
oeisdata/seq/A006/A006730.seq
df3e21ccbce7fb2223b313bda82c99a7
A006731
Site percolation series for square lattice.
[ "1", "2", "4", "7", "12", "20", "33", "53", "85", "133", "210", "322", "505", "759", "1192", "1748", "2782", "3931", "6476", "8579", "15216", "17847", "36761", "33612", "93961", "47282", "262987", "-16105", "827382", "-571524", "2936705", "-3661626", "11507775", "-18880652", "48169220", "-90436605" ]
[ "sign" ]
20
0
2
[ "A006731", "A056532" ]
[ "M1055" ]
N. J. A. Sloane, Simon Plouffe
2019-10-04T07:39:58
oeisdata/seq/A006/A006731.seq
d43cc77fed75bd403cd715c0a6823e95
A006732
Series for first parallel moment of square lattice.
[ "0", "2", "8", "22", "52", "112", "228", "442", "832", "1516", "2720", "4754", "8264", "14000", "23824", "39318", "66052", "106282", "177884", "277936", "469384", "703924", "1225052", "1718226", "3203156", "3974696", "8551248", "8307370", "23950704", "13195606", "72779892", "-1798186", "246605280", "-165440790", "935635244", "-1166043794", "3896720688", "-6470965954", "17297466660", "-33101156302", "79718300900", "-163586078926" ]
[ "sign" ]
17
0
2
null
[ "M1837" ]
N. J. A. Sloane, Simon Plouffe
2019-10-04T07:40:10
oeisdata/seq/A006/A006732.seq
4ed822b363cd1cf5c326f22c226f66bf
A006733
Series for second parallel moment of square lattice (eventually changes sign).
[ "0", "2", "16", "68", "220", "608", "1520", "3526", "7756", "16302", "33172", "65378", "126224", "237600", "441776", "802820", "1451932", "2563356", "4544304", "7818078", "13684784", "22938278", "39986208", "64996080", "114280984", "177912196", "322438072", "467942962", "909533348", "1162410740", "2614286452", "2595422914", "7869393556", "4348425126", "25625330524", "-1054012626", "92617456680", "-64842762130", "373042426296" ]
[ "sign" ]
20
0
2
null
[ "M2087" ]
N. J. A. Sloane, Simon Plouffe
2019-10-04T07:40:47
oeisdata/seq/A006/A006733.seq
603d839bc2d790568fbe7f8ca182baf7
A006734
Series for second perpendicular moment of square lattice.
[ "0", "2", "8", "24", "60", "136", "288", "582", "1132", "2138", "3940", "7114", "12632", "22080", "38160", "65056", "110172", "184032", "306968", "503650", "831408", "1340338", "2201840", "3479116", "5733312", "8814468", "14772040", "21734370", "37997724", "51650456", "98952836", "115227474", "266750996", "223323542", "768153044", "261658998", "2443777216", "-717803658", "8754481712", "-8229926352", "35018197920", "-51106610852" ]
[ "sign" ]
17
0
2
null
[ "M1839" ]
N. J. A. Sloane, Simon Plouffe
2019-10-04T07:40:55
oeisdata/seq/A006/A006734.seq
fccca9569c38c21bd78642cc986b1b8c
A006735
Bond percolation series for hexagonal net.
[ "1", "-1", "-4", "-12", "-45", "-188", "-835", "-3849", "-18242", "-88265", "-434295", "-2165198", "-10915089", "-55534781", "-284708699", "-1470350760", "-7628363273", "-39878267745", "-208458228964", "-1103369168956", "-5771541600014" ]
[ "sign" ]
12
0
3
[ "A006735", "A030131" ]
null
N. J. A. Sloane.
2017-02-19T13:52:24
oeisdata/seq/A006/A006735.seq
a365e46f52d6dce8d846d7969061ab17
A006736
Series for first parallel moment of hexagonal lattice.
[ "0", "4", "24", "104", "384", "1284", "4012", "11924", "34100", "94584", "255852", "677850", "1764482", "4523924", "11447870", "28636218", "70907326", "173991368", "423469988", "1023162920", "2455645268", "5858183260", "13898041838", "32804047708", "77067740230" ]
[ "nonn" ]
19
0
2
[ "A006736", "A006737", "A006803", "A006809" ]
[ "M3597" ]
N. J. A. Sloane, Simon Plouffe
2019-10-04T07:41:01
oeisdata/seq/A006/A006736.seq
a591c53e2fcac02766fcf045bc9748de
A006737
Series for second parallel moment of hexagonal lattice.
[ "0", "6", "68", "442", "2218", "9528", "36834", "131856", "445000", "1433294", "4444006", "13349510", "39041224", "111583236", "312618368", "860662498", "2333112020", "6238124024", "16474149036", "43023953304", "111230237224", "284926172100", "723731637254" ]
[ "nonn" ]
22
0
2
[ "A006736", "A006737", "A006738", "A006803", "A006809" ]
[ "M4275" ]
N. J. A. Sloane, Simon Plouffe
2019-10-04T07:41:08
oeisdata/seq/A006/A006737.seq
d22f7d362ec5293a5dd3ef05f4448a55
A006738
Series for second perpendicular moment of hexagonal lattice.
[ "0", "2", "12", "54", "206", "712", "2294", "7024", "20656", "58842", "163250", "443062", "1180156", "3092964", "7993116", "20401250", "51502616", "128748512", "319010540", "784179992", "1913668608", "4639155964", "11178566462", "26784974870", "63851541584" ]
[ "nonn" ]
21
0
2
[ "A006736", "A006737", "A006738", "A006803", "A006809" ]
[ "M2024" ]
N. J. A. Sloane, Simon Plouffe
2019-10-04T07:41:17
oeisdata/seq/A006/A006738.seq
5278a3338aa9415f2dfbc6845490dda5
A006739
Site percolation series for hexagonal lattice.
[ "1", "3", "7", "15", "31", "62", "122", "235", "448", "842", "1572", "2904", "5341", "9743", "17718", "32009", "57701", "103445", "185165", "329904", "587136", "1040674", "1843300", "3253020", "5738329", "10090036", "17736533", "31086416", "54484239", "95220744", "166451010", "290209573" ]
[ "nonn" ]
27
0
2
null
[ "M2654" ]
N. J. A. Sloane, Simon Plouffe
2024-02-11T06:45:07
oeisdata/seq/A006/A006739.seq
f0e7dd69788e8634e454329b70e9d978
A006740
Series for first parallel moment of hexagonal lattice.
[ "0", "4", "20", "68", "196", "512", "1256", "2936", "6628", "14528", "31140", "65414", "135276", "275656", "555216", "1105726", "2182380", "4268906", "8290740", "15984420", "30638312", "58369924", "110665328", "208734268", "392103508", "733311754", "1366650536", "2537201920" ]
[ "nonn" ]
21
0
2
null
[ "M3563" ]
N. J. A. Sloane, Simon Plouffe
2019-10-04T07:41:31
oeisdata/seq/A006/A006740.seq
21de03ed6d481718c1fbebdd48916657
A006741
Series for second parallel moment of hexagonal lattice.
[ "0", "6", "60", "314", "1240", "4166", "12600", "35324", "93576", "236944", "578764", "1371478", "3169380", "7165478", "15901324", "34705018", "74661832", "158529158", "332756408", "691084378", "1421836528", "2899678894", "5867341452", "11784640984", "23512608484" ]
[ "nonn" ]
21
0
2
null
[ "M4269" ]
N. J. A. Sloane, Simon Plouffe
2019-10-04T07:41:39
oeisdata/seq/A006/A006741.seq
af530790e3b82313ab9ce6f35c714642
A006742
Series for second perpendicular moment of hexagonal lattice.
[ "2", "12", "46", "144", "402", "1040", "2548", "5992", "13632", "30220", "65486", "139404", "291770", "602908", "1229242", "2482792", "4959014", "9836840", "19323246", "37773464", "73182570", "141345292", "270647584", "517513972", "980893354" ]
[ "sign" ]
27
1
1
null
[ "M2020" ]
N. J. A. Sloane, Simon Plouffe
2019-10-05T09:15:19
oeisdata/seq/A006/A006742.seq
ff0afb2e7d7a9093efab5db1f5195882
A006743
Number of convex polygons of length 2n on honeycomb, or EG-convex polyominoes.
[ "1", "0", "3", "2", "10", "14", "40", "74", "176", "358", "798", "1670", "3626", "7638", "16366", "34462", "73230", "153830", "324896", "680514", "1430336", "2987310", "6253712", "13025954", "27176052", "56465878", "117458820", "243507250", "505239264", "1045301486" ]
[ "nonn", "easy", "nice" ]
25
3
3
null
[ "M2255" ]
Simon Plouffe, N. J. A. Sloane
2018-08-28T12:07:32
oeisdata/seq/A006/A006743.seq
5545a8579137fd47e27e7bb9619563ee
A006744
Number of n-step self-avoiding walks on a Manhattan lattice.
[ "1", "2", "4", "7", "13", "24", "44", "77", "139", "250", "450", "788", "1403", "2498", "4447", "7782", "13769", "24363", "43106", "75396", "132865", "234171", "412731", "721433", "1267901", "2228666", "3917654", "6843596", "12004150", "21059478", "36947904", "64506130", "112983428", "197921386", "346735329", "605046571", "1058544744", "1852200487" ]
[ "nonn", "walk" ]
37
1
2
[ "A006744", "A117633" ]
[ "M1073" ]
Simon Plouffe
2020-02-18T03:40:11
oeisdata/seq/A006/A006744.seq
2ea32fa73d5905ab9979afae23fdcde5
A006745
Number of indefinitely growing n-step self-avoiding walks on Manhattan lattice.
[ "1", "2", "4", "7", "13", "24", "43", "77", "139", "249", "443", "786", "1400", "2486", "4395", "7758", "13732", "24251", "42710", "75154", "132487", "233173", "409617", "719157", "1264303", "2219916", "3892603", "6822808", "11970965", "20983162", "36742831", "64319064" ]
[ "nonn", "walk" ]
15
1
2
null
[ "M1071" ]
Simon Plouffe
2017-07-13T10:35:00
oeisdata/seq/A006/A006745.seq
59593f55611f2bc877a7491a9c386555
A006746
Number of axially symmetric polyominoes with n cells.
[ "0", "0", "0", "1", "2", "6", "9", "23", "38", "90", "147", "341", "564", "1294", "2148", "4896", "8195", "18612", "31349", "70983", "120357", "271921", "463712", "1045559", "1792582", "4034832", "6950579", "15619507", "27023509", "60638559", "105320716", "236006955", "411364068", "920626423", "1609836928" ]
[ "nonn" ]
49
1
5
[ "A000105", "A001168", "A006746", "A006747", "A006748", "A006749", "A030227", "A056877", "A056878", "A142886", "A144553", "A144554", "A349328", "A349329", "A361625" ]
[ "M1573" ]
N. J. A. Sloane
2023-04-15T06:25:50
oeisdata/seq/A006/A006746.seq
01ea448800fb95776695e722a1c7b5f7
A006747
Number of rotationally symmetric polyominoes with n cells (that is, polyominoes with exactly the symmetry group C_2 generated by a 180-degree rotation).
[ "0", "0", "0", "1", "1", "5", "4", "18", "19", "73", "73", "278", "283", "1076", "1090", "4125", "4183", "15939", "16105", "61628", "62170", "239388", "240907", "932230", "936447", "3641945", "3651618", "14262540", "14277519", "55987858", "55961118", "220223982", "219813564", "867835023", "865091976", "3425442681" ]
[ "nonn" ]
75
1
6
[ "A000105", "A001168", "A006746", "A006747", "A006748", "A006749", "A056877", "A056878", "A142886", "A144553", "A144554", "A234008", "A348402", "A348403", "A348404", "A351615", "A351616" ]
[ "M3741" ]
N. J. A. Sloane
2023-10-19T12:10:24
oeisdata/seq/A006/A006747.seq
c581ea3bfc05e85d59af75abff52444d
A006748
Number of diagonally symmetric polyominoes with n cells.
[ "0", "0", "1", "0", "2", "2", "7", "5", "26", "22", "91", "79", "326", "301", "1186", "1117", "4352", "4212", "16119", "15849", "60174", "60089", "226146", "228426", "854803", "872404", "3247207", "3342579", "12389106", "12850662", "47448984", "49544820", "182338754", "191529007", "702807040", "742163178", "2716205709", "2882119756" ]
[ "nonn" ]
54
1
5
[ "A000105", "A001168", "A006746", "A006747", "A006748", "A006749", "A056877", "A056878", "A142886", "A144553", "A144554" ]
[ "M0366" ]
N. J. A. Sloane
2023-04-16T12:32:40
oeisdata/seq/A006/A006748.seq
97e7cc59a7d4b5d662a049609178cdd6
A006749
Number of asymmetric polyominoes with n cells.
[ "0", "0", "0", "1", "5", "20", "84", "316", "1196", "4461", "16750", "62878", "237394", "899265", "3422111", "13069026", "50091095", "192583152", "742560511", "2870523142", "11122817672", "43191285751", "168046076423", "654997492842", "2557223459805", "9999080270766", "39152997087077", "153511067364760" ]
[ "nonn", "nice" ]
38
1
5
[ "A000105", "A001168", "A006746", "A006747", "A006748", "A006749", "A056877", "A056878", "A142886", "A144553", "A144554" ]
[ "M3906" ]
N. J. A. Sloane
2024-03-21T21:02:38
oeisdata/seq/A006/A006749.seq
15f2f3f497106bb4b48efbab575565d2
A006750
Coefficients of Legendre polynomials.
[ "8", "88", "2992", "23408", "354200", "2641320", "156641760", "1159149024", "17161845272", "127234370120", "3780912959824", "28153740304144", "420295123111864", "3144786170643656", "377374340477238720", "2836750530124023744" ]
[ "nonn" ]
19
2
1
null
[ "M4564" ]
N. J. A. Sloane.
2022-09-08T08:44:35
oeisdata/seq/A006/A006750.seq
d07bcfbf038517264d8cced4af4d4ff9
A006751
Describe the previous term! (method A - initial term is 2).
[ "2", "12", "1112", "3112", "132112", "1113122112", "311311222112", "13211321322112", "1113122113121113222112", "31131122211311123113322112", "132113213221133112132123222112", "11131221131211132221232112111312111213322112", "31131122211311123113321112131221123113111231121123222112" ]
[ "nonn", "base", "easy", "nice" ]
72
1
1
[ "A001140", "A001141", "A001143", "A001145", "A001151", "A001154", "A001155", "A005150", "A006715", "A006751", "A045918", "A088203" ]
[ "M2052" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006751.seq
c60a59aa071f11db3e2e8517ff5d43b0
A006752
Decimal expansion of Catalan's constant 1 - 1/9 + 1/25 - 1/49 + 1/81 - ...
[ "9", "1", "5", "9", "6", "5", "5", "9", "4", "1", "7", "7", "2", "1", "9", "0", "1", "5", "0", "5", "4", "6", "0", "3", "5", "1", "4", "9", "3", "2", "3", "8", "4", "1", "1", "0", "7", "7", "4", "1", "4", "9", "3", "7", "4", "2", "8", "1", "6", "7", "2", "1", "3", "4", "2", "6", "6", "4", "9", "8", "1", "1", "9", "6", "2", "1", "7", "6", "3", "0", "1", "9", "7", "7", "6", "2", "5", "4", "7", "6", "9", "4", "7", "9", "3", "5", "6", "5", "1", "2", "9", "2", "6", "1", "1", "5", "1", "0", "6", "2", "4", "8", "5", "7", "4" ]
[ "nonn", "cons", "easy" ]
252
0
1
[ "A006752", "A014538", "A054543", "A104338", "A118323", "A153069", "A153070", "A294970", "A294971" ]
[ "M4593" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006752.seq
eea8b193de0a7366659767eca097d744
A006753
Smith (or joke) numbers: composite numbers n such that sum of digits of n = sum of digits of prime factors of n (counted with multiplicity).
[ "4", "22", "27", "58", "85", "94", "121", "166", "202", "265", "274", "319", "346", "355", "378", "382", "391", "438", "454", "483", "517", "526", "535", "562", "576", "588", "627", "634", "636", "645", "648", "654", "663", "666", "690", "706", "728", "729", "762", "778", "825", "852", "861", "895", "913", "915", "922", "958", "985", "1086", "1111", "1165", "1219" ]
[ "nonn", "base", "nice", "easy" ]
102
1
1
[ "A002808", "A006753", "A007953", "A019506", "A050218", "A050224", "A050255", "A098834", "A098840", "A103123", "A103126", "A104166", "A104171", "A104390", "A104391", "A202387", "A202388" ]
[ "M3582" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006753.seq
a5ff660421602ec8d39e3ed8bd9920b1
A006754
The generalized Conway-Guy sequence w^{0}.
[ "0", "3", "5", "6", "7", "14", "25", "45", "84", "162", "310", "595", "1165", "2285", "4486", "8810", "17310", "34310", "68025", "134885", "267485" ]
[ "nonn", "more" ]
19
0
2
[ "A005318", "A006754", "A006755", "A006756", "A006757", "A195683", "A195684" ]
[ "M2390" ]
N. J. A. Sloane
2017-10-13T16:39:37
oeisdata/seq/A006/A006754.seq
fae2b86774526c23964a36b65f315cdc
A006755
The generalized Conway-Guy sequence w^{1}.
[ "0", "2", "3", "4", "8", "14", "25", "47", "86", "164", "314", "603", "1159", "2271", "4456", "8748", "17182", "33761", "66919", "132679", "263087" ]
[ "nonn", "more" ]
17
0
2
[ "A005318", "A006754", "A006755", "A006756", "A006757", "A195683", "A195684" ]
[ "M0590" ]
N. J. A. Sloane.
2019-11-16T03:50:00
oeisdata/seq/A006/A006755.seq
9aa30e66b6397b0467437b24d715d692
A006756
The generalized Conway-Guy sequence w^{2}.
[ "0", "4", "5", "6", "8", "16", "27", "49", "92", "168", "320", "613", "1177", "2262", "4432", "8696", "17072", "33531", "65885", "130593", "258924" ]
[ "nonn", "more" ]
16
0
2
[ "A005318", "A006754", "A006755", "A006756", "A006757", "A195683", "A195684" ]
[ "M3238" ]
N. J. A. Sloane.
2019-11-16T03:50:23
oeisdata/seq/A006/A006756.seq
8629fd8c9a63cc37d4531da135decb3c
A006757
The generalized Conway-Guy sequence w^{3}.
[ "0", "8", "10", "11", "12", "16", "32", "54", "97", "183", "334", "636", "1218", "2339", "4495", "8807", "17280", "33924", "66630", "130921", "259503" ]
[ "nonn", "more" ]
16
0
2
[ "A005318", "A006754", "A006755", "A006756", "A006757", "A195683", "A195684" ]
[ "M4476" ]
N. J. A. Sloane.
2017-10-13T08:53:16
oeisdata/seq/A006/A006757.seq
f8866a3fd019da6f846f596eb207d4c9
A006758
Number of strictly 2-dimensional one-sided polyominoes with n cells.
[ "0", "0", "0", "1", "6", "17", "59", "195", "703", "2499", "9188", "33895", "126758", "476269", "1802311", "6849776", "26152417", "100203193", "385221142", "1485200847", "5741256763", "22245940544", "86383382826", "336093325057", "1309998125639", "5114451441105", "19998172734785", "78306011677181", "307022182222505", "1205243866707467", "4736694001644861", "18635412907198669" ]
[ "nonn" ]
58
0
5
[ "A000988", "A006758", "A195738" ]
[ "M4114" ]
N. J. A. Sloane
2021-03-14T20:46:13
oeisdata/seq/A006/A006758.seq
aedb515f06efabcc8389312932459c13
A006759
Number of one-sided strictly 3-dimensional polyominoes with n cells.
[ "0", "0", "0", "3", "17", "131", "915", "6553", "47026", "341888", "2505449", "18534827", "138224058", "1038594326", "7856087894", "59782042225", "457359506070", "3515816578512", "27143401299351", "210372490707568" ]
[ "nonn", "more" ]
29
1
4
[ "A006759", "A195738" ]
[ "M3038" ]
N. J. A. Sloane
2023-12-26T06:38:38
oeisdata/seq/A006/A006759.seq
806d3c01cd0a88ec1c7b3aa75fe43804
A006760
Number of one-sided 4-dimensional polyominoes with n cells.
[ "0", "0", "0", "0", "4", "52", "709", "8946", "108761", "1296258", "15308897" ]
[ "nonn", "more" ]
13
1
5
[ "A006760", "A195738" ]
[ "M3688" ]
N. J. A. Sloane.
2017-07-19T06:17:01
oeisdata/seq/A006/A006760.seq
8125c904b986cf75be8b387fd47e6c2e
A006761
Number of one-sided, properly 5-dimensional polyominoes with n cells.
[ "0", "0", "0", "0", "0", "7", "153", "3350", "65973", "1215851", "21466784" ]
[ "nonn", "more" ]
26
1
6
[ "A006761", "A195738", "A290305" ]
[ "M4460" ]
N. J. A. Sloane
2023-08-19T16:11:54
oeisdata/seq/A006/A006761.seq
00b336b724b7819b4b18942333b5b9d0
A006762
Number of strictly 2-dimensional fixed polyominoes with n cells.
[ "0", "0", "4", "17", "61", "214", "758", "2723", "9908", "36444", "135266", "505859", "1903888", "7204872", "27394664", "104592935", "400795842", "1540820540", "5940738674", "22964779658", "88983512781", "345532572676", "1344372335522", "5239988770266", "20457802016009", "79992676367106", "313224032098242", "1228088671826971" ]
[ "nonn" ]
26
1
3
[ "A001168", "A006762", "A195739" ]
[ "M3534" ]
N. J. A. Sloane
2019-09-06T10:52:28
oeisdata/seq/A006/A006762.seq
53ae326036d6f0fc5f601d61f06b2e9d
A006763
Number of fixed properly-3-dimensional polyominoes with n cells.
[ "0", "0", "0", "32", "348", "2836", "21225", "154741", "1123143", "8185403", "60088748", "444688325", "3317057654", "24925158492", "188543716451", "1434760675947", "10976610064899", "84379534826376", "651441493579872" ]
[ "nonn", "more" ]
25
1
4
[ "A006763", "A195739" ]
[ "M5232" ]
N. J. A. Sloane
2019-09-22T07:17:31
oeisdata/seq/A006/A006763.seq
9caf44393d32028aef58b52342f4ca42
A006764
Number of fixed properly-4-dimensional polyominoes with n cells.
[ "0", "0", "0", "0", "400", "8640", "129288", "1688424", "20762073", "248384816", "2937307716", "34618858308" ]
[ "nonn", "more" ]
20
1
5
[ "A000105", "A006764", "A195739" ]
[ "M5451" ]
N. J. A. Sloane.
2019-01-12T02:32:13
oeisdata/seq/A006/A006764.seq
c8afd5123e40e9e7760fa70bf7cf4042
A006765
Number of strictly 2-dimensional polyominoes with n cells.
[ "0", "0", "1", "4", "11", "34", "107", "368", "1284", "4654", "17072", "63599", "238590", "901970", "3426575", "13079254", "50107908", "192622051", "742624231", "2870671949", "11123060677", "43191857687", "168047007727", "654999700402", "2557227044763", "9999088822074", "39153010938486", "153511100594602", "602621953061977", "2368347037571251", "9317706529987949", "36695016991712878" ]
[ "nonn" ]
46
1
4
[ "A000105", "A006765", "A049429", "A049430" ]
[ "M3421" ]
N. J. A. Sloane
2023-04-15T12:27:23
oeisdata/seq/A006/A006765.seq
9fdf6485e34396dba0cfcd3cd07e614b
A006766
Number of 3-dimensional polyominoes with n cells.
[ "0", "0", "0", "2", "11", "77", "499", "3442", "24128", "173428", "1262464", "9307494" ]
[ "hard", "nonn" ]
19
1
4
[ "A006766", "A049429", "A049430" ]
[ "M2005" ]
N. J. A. Sloane.
2017-09-21T09:03:12
oeisdata/seq/A006/A006766.seq
28ad9dafa37dc6fa9a03e99baef93510
A006767
Number of 4-dimensional polyominoes with n cells.
[ "0", "0", "0", "0", "3", "35", "412", "4888", "57122", "667959", "7799183" ]
[ "nonn", "more" ]
17
1
5
[ "A006767", "A049429", "A049430" ]
[ "M3137" ]
N. J. A. Sloane.
2019-01-12T02:35:13
oeisdata/seq/A006/A006767.seq
6305186ee967acc033be766a29da9ae8
A006768
Number of 5-dimensional polyominoes with n cells.
[ "0", "0", "0", "0", "0", "6", "104", "2009", "36585", "647680", "11173880" ]
[ "nonn", "more" ]
18
1
6
[ "A006768", "A049429", "A049430" ]
[ "M4293" ]
N. J. A. Sloane.
2017-09-21T09:03:12
oeisdata/seq/A006/A006768.seq
c9ef813fd020f2dbdf9516af8ab8bc71
A006769
Elliptic divisibility sequence associated with elliptic curve "37a1": y^2 + y = x^3 - x and multiples of the point (0,0).
[ "0", "1", "1", "-1", "1", "2", "-1", "-3", "-5", "7", "-4", "-23", "29", "59", "129", "-314", "-65", "1529", "-3689", "-8209", "-16264", "83313", "113689", "-620297", "2382785", "7869898", "7001471", "-126742987", "-398035821", "1687054711", "-7911171596", "-47301104551", "43244638645" ]
[ "sign", "easy", "nice" ]
142
0
6
[ "A006720", "A006769", "A028941", "A050512", "A051138", "A178072", "A278314" ]
[ "M0157" ]
Michael Somos, Jul 16 1999
2025-01-05T19:51:34
oeisdata/seq/A006/A006769.seq
d295834f387d70ca5cbe0eb299ef013a
A006770
Number of fixed n-celled polyominoes which need only touch at corners.
[ "1", "4", "20", "110", "638", "3832", "23592", "147941", "940982", "6053180", "39299408", "257105146", "1692931066", "11208974860", "74570549714", "498174818986", "3340366308393" ]
[ "nonn", "hard", "more" ]
35
1
2
[ "A006770", "A030222", "A366767" ]
[ "M3565" ]
N. J. A. Sloane.
2025-02-16T08:32:30
oeisdata/seq/A006/A006770.seq
ee19e49477b4c61f1434d2d47dcf3483
A006771
Exponential self-convolution of numbers of trees on n nodes.
[ "1", "2", "4", "8", "18", "46", "128", "372", "1174", "3820", "13170", "46714", "172490", "652758", "2547196", "10156810", "41495158", "172810254", "734132414", "3171713642", "13933910250", "62121022408", "280907384318", "1286617710114", "5964793344934", "27961159869700", "132441462312280", "633354027835730" ]
[ "nonn" ]
6
0
2
[ "A000055", "A006771" ]
null
N. J. A. Sloane.
2016-10-04T15:37:13
oeisdata/seq/A006/A006771.seq
728ab465f3058ecf3d135376e1e5fdf0
A006772
Sum of spans of 2n-step polygons on square lattice.
[ "0", "1", "3", "14", "70", "370", "2028", "11452", "66172", "389416", "2326202", "14070268", "86010680", "530576780", "3298906810", "20653559846", "130099026600", "823979294284", "5244162058026", "33523117491920", "215150177410088", "1385839069134800", "8956173544332434", "58056703069399056", "377396656568011618", "2459614847765495754", "16068572108927106202" ]
[ "nonn" ]
19
1
3
[ "A002931", "A006772", "A006773", "A232103", "A302336", "A302337" ]
[ "M2971" ]
N. J. A. Sloane
2018-11-09T16:23:07
oeisdata/seq/A006/A006772.seq
d82f20f9677e0e21bb49cf033b271fa6
A006773
Sum of squared spans of 2n-step polygons on square lattice.
[ "0", "1", "5", "30", "186", "1164", "7344", "46732", "299604", "1932900", "12537542", "81705782", "534663812", "3511466838", "23136724382", "152888000934", "1012925595468", "6726766841438", "44767880394634", "298522284224824", "1994187071224056", "13343458013982572", "89420609914983270", "600088861692380354", "4032377457462571694", "27129080022839863318", "182726605700552001998" ]
[ "nonn" ]
9
1
3
[ "A006772", "A006773" ]
[ "M3959" ]
N. J. A. Sloane
2018-11-09T16:23:01
oeisdata/seq/A006/A006773.seq
7dccc560f939a81d315b2a41240ab077
A006774
Number of 2n-step polygons on honeycomb.
[ "1", "0", "0", "1", "0", "3", "2", "12", "18", "65", "138", "432", "1074", "3231", "8718", "25999", "73650", "220215", "643546", "1937877", "5783700", "17564727", "53222094", "163009086", "499634508", "1542392088", "4770925446", "14832934031", "46227584010", "144632622552", "453628244950" ]
[ "nonn" ]
22
0
6
null
[ "M2257" ]
N. J. A. Sloane
2022-09-07T14:55:59
oeisdata/seq/A006/A006774.seq
b5b3c95bd1610a310c00cf2e6acdd8f0
A006775
Erroneous version of A309982.
[ "1", "2", "4", "8", "16", "31", "61", "115", "213", "388", "691", "1218", "2110", "3617", "6113", "10238", "16945", "27802", "45180", "72838", "116479", "184936", "291556", "456694", "710907", "1100192", "1693123", "2591830", "3947417", "5982953" ]
[ "dead" ]
17
1
2
null
[ "M1121" ]
null
2019-09-01T10:13:25
oeisdata/seq/A006/A006775.seq
99c43eedafcbbf3c4ae05eaa6b717855
A006776
Number of n-step spirals on hexagonal lattice.
[ "1", "3", "8", "20", "47", "106", "230", "479", "973", "1924", "3712", "7021", "13034", "23780", "42732", "75703", "132360", "228664", "390611", "660296", "1105321", "1833358", "3014694", "4917036", "7958127", "12786252", "20401469", "32337878", "50936233", "79750436", "124149022", "192204697", "296001288", "453548269", "691574373", "1049590078" ]
[ "nonn" ]
16
1
2
null
[ "M2738" ]
N. J. A. Sloane.
2019-08-26T04:27:11
oeisdata/seq/A006/A006776.seq
7777a9428e1b03cedf8af36a83e38b70
A006777
Number of n-step spirals on hexagonal lattice.
[ "1", "2", "4", "8", "14", "26", "43", "74", "120", "197", "311", "495", "768", "1189", "1811", "2748", "4116", "6136", "9058", "13299", "19370", "28069", "40399", "57856", "82374", "116736", "164574", "231007", "322749", "449089", "622263", "858935", "1181048", "1618209", "2209299", "3006273", "4077285", "5512650", "7430440", "9986147" ]
[ "nonn" ]
23
1
2
[ "A006777", "A006778", "A309982" ]
[ "M1098" ]
N. J. A. Sloane
2022-04-05T08:22:43
oeisdata/seq/A006/A006777.seq
60622c730af3cfe93fade1f0602b4ad2
A006778
Number of n-step spirals on hexagonal lattice.
[ "1", "3", "7", "15", "31", "59", "110", "198", "347", "592", "997", "1641", "2666", "4266", "6741", "10525", "16268", "24882", "37717", "56683", "84504", "125031", "183716", "268125", "388873", "560647", "803723", "1146013", "1625731", "2294964", "3224588", "4510552", "6282295", "8714035", "12039319", "16570278", "22723025" ]
[ "nonn" ]
25
1
2
[ "A006776", "A006777", "A006778" ]
[ "M2652" ]
N. J. A. Sloane
2022-04-05T08:22:55
oeisdata/seq/A006/A006778.seq
6a4a721e5095276ed074a847ff5bc274
A006779
Number of n-step spirals on cubic lattice.
[ "1", "6", "18", "54", "150", "426", "1158", "3204", "8682", "23724", "64194", "174378", "470856", "1274430", "3434826", "9272346", "24953004", "67230288", "180705126", "486152604", "1305430884", "3507947838", "9412114986", "25268587338", "67752451146", "181754458194", "487060621596", "1305761069730", "3497441209182" ]
[ "nonn", "walk" ]
17
0
2
null
[ "M4121" ]
N. J. A. Sloane
2019-08-26T03:18:30
oeisdata/seq/A006/A006779.seq
510412bc357199368ac157fd00f431ec
A006780
Number of n-step anisotropic spirals on cubic lattice.
[ "1", "6", "24", "90", "324", "1166", "4138", "14730", "51992", "183898", "646980", "2279702", "8002976", "28127418", "98585096", "345848306", "1210704274", "4241348770", "14833284544", "51907058582", "181392476966", "634197818374", "2214804822718", "7737946227490" ]
[ "nonn", "more" ]
23
0
2
null
[ "M4163" ]
N. J. A. Sloane
2025-02-03T13:41:15
oeisdata/seq/A006/A006780.seq
d702a2ca5378912d49c2fd31fe60d7a7
A006781
Number of polygons of length 4n on Manhattan lattice.
[ "1", "2", "7", "32", "168", "970", "5984", "38786", "261160", "1812630", "12895360", "93638634", "691793872", "5186869122", "39388514522", "302457399674", "2345362579172", "18345337742960", "144612959167806", "1147920496989270", "9169516892088470" ]
[ "nonn", "walk", "nice" ]
17
1
2
null
[ "M1788" ]
N. J. A. Sloane
2018-10-02T11:15:18
oeisdata/seq/A006/A006781.seq
099201a0ec92ad44fb792d2b78239c3b
A006782
Number of polygons of length 4n on L-lattice.
[ "1", "0", "1", "2", "9", "36", "154", "684", "3128", "14666", "70258", "342766", "1698625", "8532410", "43368153", "222729492", "1154455161", "6033034032", "31760434883", "168311948410", "897327111964", "4810159375532", "25914118276362" ]
[ "nonn", "more" ]
40
1
4
[ "A002931", "A006781", "A006782" ]
[ "M1930" ]
N. J. A. Sloane
2019-05-18T07:23:19
oeisdata/seq/A006/A006782.seq
88f82a565c62b72e1dcab501520a665b
A006783
Maximally extended polygons of length 2n on cubic lattice.
[ "3", "22", "201", "2160", "24680", "285384", "3278484", "37154172" ]
[ "nonn", "more" ]
11
1
1
null
[ "M3094" ]
N. J. A. Sloane
2015-08-02T14:56:54
oeisdata/seq/A006/A006783.seq
3c212de0e68ac6ad3e0b3761fa57c21f
A006784
Engel expansion of Pi.
[ "1", "1", "1", "8", "8", "17", "19", "300", "1991", "2492", "7236", "10586", "34588", "63403", "70637", "1236467", "5417668", "5515697", "5633167", "7458122", "9637848", "9805775", "41840855", "58408380", "213130873", "424342175", "2366457522", "4109464489", "21846713216", "27803071890", "31804388758", "32651669133" ]
[ "nonn", "nice", "easy" ]
73
1
4
null
[ "M4475" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:30
oeisdata/seq/A006/A006784.seq
d1709dddba9aab52b53e33d12e992fea
A006785
Number of triangle-free graphs on n vertices.
[ "1", "2", "3", "7", "14", "38", "107", "410", "1897", "12172", "105071", "1262180", "20797002", "467871369", "14232552452", "581460254001", "31720840164950" ]
[ "nonn", "more" ]
60
1
2
[ "A006785", "A024607", "A283417" ]
[ "M0841" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006785.seq
84f8728dfacfe505fe7f361e74ca85c5
A006786
Number of squarefree graphs on n vertices.
[ "1", "2", "4", "8", "18", "44", "117", "351", "1230", "5069", "25181", "152045", "1116403", "9899865", "104980369", "1318017549", "19427531763", "333964672216", "6660282066936" ]
[ "nonn", "more" ]
47
1
2
[ "A000088", "A006786", "A039751", "A077269", "A300756", "A345249" ]
[ "M1149" ]
N. J. A. Sloane.
2025-02-16T08:32:30
oeisdata/seq/A006/A006786.seq
1e0c656993fbf11698f414e25a99b16c
A006787
Number of n-node graphs with no cycles of length less than 5.
[ "1", "2", "3", "6", "11", "23", "48", "114", "293", "869", "2963", "12066", "58933", "347498", "2455693", "20592932", "202724920", "2322206466", "30743624324", "468026657815", "8161170076257" ]
[ "nonn", "more" ]
47
1
2
[ "A000066", "A000088", "A006787", "A054760", "A126757", "A128236", "A128237", "A159847", "A300705" ]
[ "M0792" ]
N. J. A. Sloane
2021-11-19T17:41:05
oeisdata/seq/A006/A006787.seq
a15e47f2dff8727180422a893ac356e5
A006788
a(n) = floor(2^(n-1)/n).
[ "1", "1", "1", "2", "3", "5", "9", "16", "28", "51", "93", "170", "315", "585", "1092", "2048", "3855", "7281", "13797", "26214", "49932", "95325", "182361", "349525", "671088", "1290555", "2485513", "4793490", "9256395", "17895697", "34636833", "67108864", "130150524", "252645135", "490853405", "954437176", "1857283155", "3616814565" ]
[ "nonn" ]
58
1
4
[ "A000048", "A006788", "A054650" ]
[ "M0712" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006788.seq
da00ce53231c90a82c1f0eb74d984068
A006789
Bessel numbers: the number of nonoverlapping partitions of an n-set into equivalence classes.
[ "1", "1", "2", "5", "14", "43", "143", "509", "1922", "7651", "31965", "139685", "636712", "3020203", "14878176", "75982829", "401654560", "2194564531", "12377765239", "71980880885", "431114329728", "2656559925883", "16825918195484", "109439943234749", "730365368850192" ]
[ "nonn" ]
101
0
3
[ "A000110", "A006789", "A086880", "A153197" ]
[ "M1462" ]
N. J. A. Sloane, Simon Plouffe
2024-08-03T02:29:49
oeisdata/seq/A006/A006789.seq
be62e2abfc0ac8ba77555082f3bfa2d7
A006790
Exponentiation of e.g.f. for trees A000055(n-1).
[ "1", "2", "5", "15", "53", "211", "938", "4582", "24349", "139671", "858745", "5628789", "39145021", "287667582", "2226033629", "18082308403", "153770703339", "1365631349757", "12638233544989", "121640399661294", "1215438543434225", "12587691428792115" ]
[ "nonn" ]
14
0
2
[ "A000055", "A006790" ]
null
N. J. A. Sloane.
2015-03-30T06:44:33
oeisdata/seq/A006/A006790.seq
a82f519550b3c05e95d9bd3021970270
A006791
Number of cyclically-5-connected planar trivalent graphs with 2n nodes.
[ "1", "0", "1", "1", "3", "4", "12", "23", "71", "187", "627", "1970", "6833", "23384", "82625", "292164", "1045329", "3750277", "13532724", "48977625", "177919099", "648145255", "2368046117", "8674199554", "31854078139", "117252592450", "432576302286", "1599320144703", "5925181102878" ]
[ "nonn" ]
25
10
5
[ "A006791", "A111358" ]
[ "M2373" ]
N. J. A. Sloane.
2019-03-21T16:48:36
oeisdata/seq/A006/A006791.seq
2ec07d2df882d71982a2ca606e9533e1
A006792
Number of n-node vertex-transitive graphs which are not Cayley graphs.
[ "2", "0", "0", "0", "0", "4", "8", "0", "4", "0", "82", "0", "0", "0", "112", "0", "132", "0", "66", "0", "1124", "0", "18170", "0", "920", "6", "4162", "0", "0", "0", "48266", "0", "242", "0", "96", "294", "0", "0" ]
[ "nonn", "more" ]
28
10
1
[ "A006792", "A006799", "A185959" ]
[ "M0009" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006792.seq
aa4ca25143bd93ff8a90c1c4ec67ac0c
A006793
Orders of vertex-transitive graphs which are not Cayley graphs.
[ "10", "12", "15", "16", "18", "20", "24", "26", "28", "30", "32", "34", "35", "36", "40", "42", "44", "45", "48", "50", "52", "54", "56", "57", "58", "60", "63", "64" ]
[ "nonn" ]
16
1
1
null
[ "M4680" ]
N. J. A. Sloane.
2017-10-18T02:45:32
oeisdata/seq/A006/A006793.seq
c1d89a266c90014186134a4087caab84
A006794
Primorial -1 primes: primes p such that -1 + product of primes up to p is prime.
[ "3", "5", "11", "13", "41", "89", "317", "337", "991", "1873", "2053", "2377", "4093", "4297", "4583", "6569", "13033", "15877", "843301", "1098133", "3267113", "4778027", "6354977", "6533299" ]
[ "nonn", "hard", "more", "nice" ]
101
1
1
[ "A002110", "A005234", "A006794", "A014545", "A018239", "A057704", "A057705" ]
[ "M2474" ]
N. J. A. Sloane
2025-03-28T04:55:26
oeisdata/seq/A006/A006794.seq
20a1f169e0addbba083d72a5281dee3b
A006795
A subclass of 2n-node trivalent planar graphs without triangles.
[ "1", "2", "9", "43", "212", "1115", "6156", "34693", "199076" ]
[ "nonn", "more" ]
11
7
2
null
[ "M1936" ]
N. J. A. Sloane.
2018-09-26T09:11:12
oeisdata/seq/A006/A006795.seq
048e99f04128411b3f61e020780a3eff
A006796
A subclass of 2n-node trivalent planar graphs without triangles.
[ "2", "3", "8", "22", "77", "285", "1259", "5863", "29322", "151308" ]
[ "nonn", "more" ]
12
6
1
null
[ "M0886" ]
N. J. A. Sloane.
2018-09-26T09:10:49
oeisdata/seq/A006/A006796.seq
c401e0a6009b1a05ba817fce89080896
A006797
A subclass of 2n-node trivalent planar graphs without triangles.
[ "1", "1", "0", "1", "2", "3", "9", "28", "97", "378", "1601", "7116" ]
[ "nonn", "more" ]
13
4
5
null
[ "M0899" ]
N. J. A. Sloane.
2018-09-26T09:13:05
oeisdata/seq/A006/A006797.seq
33146be8e613966aecafd8af7706dc41
A006798
A subclass of 2n-node trivalent planar graphs without triangles.
[ "1", "1", "4", "13", "58", "279", "1406", "7525" ]
[ "nonn", "more" ]
10
8
3
null
[ "M3470" ]
N. J. A. Sloane.
2018-09-26T09:13:45
oeisdata/seq/A006/A006798.seq
82c3289c6375b1a3628482a12e2745e0
A006799
Number of vertex-transitive graphs with n nodes.
[ "1", "2", "2", "4", "3", "8", "4", "14", "9", "22", "8", "74", "14", "56", "48", "286", "36", "380", "60", "1214", "240", "816", "188", "15506", "464", "4236", "1434", "25850", "1182", "46308", "2192", "677402", "6768", "132580", "11150", "1963202", "14602", "814216", "48462", "13104170", "52488", "9462226", "99880", "39134640", "399420", "34333800", "364724" ]
[ "nonn", "nice", "hard" ]
49
1
2
[ "A006792", "A006793", "A006799", "A006800", "A185959", "A319367" ]
[ "M0302" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006799.seq
02b102f1e8b6c7d763cf81e8ffd94c77
A006800
Number of connected vertex-transitive graphs with n nodes.
[ "1", "1", "1", "2", "2", "5", "3", "10", "7", "18", "7", "64", "13", "51", "44", "272", "35", "365", "59", "1190", "235", "807", "187", "15422", "461", "4221", "1425", "25792", "1181", "46236", "2191", "677116", "6759", "132543", "11144", "1962756", "14601", "814155", "48447", "13102946", "52487", "9461929", "99879", "39133822", "399365", "34333611", "364723" ]
[ "nonn", "nice" ]
37
1
4
[ "A006799", "A006800", "A319368" ]
[ "M0345" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006800.seq
ab87d581340c281cb9ab1c6a45cd0bb9