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1999-12-11 03:00:00
2025-04-28 00:58:08
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A005401
High-temperature series for Heisenberg model susceptibility on square lattice.
[ "4", "16", "64", "416", "4544", "23488", "-207616", "4205056", "198295552", "-2574439424", "-112886362112", "3567419838464", "94446596145152", "-5636771173998592", "-80736001427931136", "11035864514607054848", "15012780903941799936", "-25650368909583695740928" ]
[ "sign" ]
22
1
1
[ "A002170", "A005399", "A005401", "A005402" ]
[ "M3519" ]
N. J. A. Sloane
2024-11-26T02:59:46
oeisdata/seq/A005/A005401.seq
ce46f7f7be0b2997b7be79bca1d21496
A005402
High temperature series for spin-1/2 Heisenberg specific heat on 2D square lattice.
[ "0", "6", "-12", "-84", "1200", "3120", "-249312", "920928", "86274816", "-1232035584", "-40970012160", "1391730516480", "20983074318336", "-1798371774277632", "-1850681724997632", "2713439169345073152", "-40045819902128750592", "-4625352042615223025664", "171173842584165886328832", "8223835353617664214695936" ]
[ "sign" ]
29
1
2
[ "A002169", "A005400", "A005401", "A005402" ]
[ "M4100" ]
N. J. A. Sloane
2024-11-25T12:15:36
oeisdata/seq/A005/A005402.seq
d718aa186d598d7ba3db0b83f64dd04b
A005403
Number of protruded partitions of n with largest part at most 2.
[ "1", "3", "5", "10", "17", "31", "53", "92", "156", "265", "445", "746", "1243", "2066", "3421", "5652", "9314", "15320", "25152", "41232", "67497", "110361", "180249", "294115", "479500", "781143", "1271675", "2068987", "3364358", "5468074", "8883329", "14425997", "23418648", "38004865", "61658326", "100007327" ]
[ "nonn" ]
14
1
2
null
[ "M2463" ]
N. J. A. Sloane.
2025-01-05T19:51:33
oeisdata/seq/A005/A005403.seq
bcc36dcdb98c34cbca70f5d429a21611
A005404
Number of protruded partitions of n with largest part at most 3.
[ "1", "3", "6", "12", "22", "42", "75", "135", "238", "416", "719", "1236", "2107", "3574", "6030", "10130", "16950", "28267", "46993", "77916", "128874", "212701", "350375", "576165", "945984", "1551009", "2539790", "4154212", "6787891", "11081022", "18074324", "29458899", "47981563", "78102314", "127060462" ]
[ "nonn" ]
21
1
2
null
[ "M2555" ]
N. J. A. Sloane.
2025-01-05T19:51:33
oeisdata/seq/A005/A005404.seq
55db22505fff2f40374829018c1bf37a
A005405
Number of protruded partitions of n with largest part at most 4.
[ "1", "3", "6", "13", "24", "47", "86", "159", "285", "509", "895", "1565", "2708", "4660", "7964", "13543", "22912", "38604", "64785", "108356", "180661", "300384", "498183", "824365", "1361302", "2243799", "3692159", "6066161", "9952786", "16309055", "26694132", "43646685", "71297770", "116366274", "189774755", "309271954", "503687536" ]
[ "nonn" ]
19
1
2
null
[ "M2565" ]
N. J. A. Sloane.
2025-01-05T19:51:33
oeisdata/seq/A005/A005405.seq
b22cc204584afa5bdfcd4cbe2220ded5
A005406
Number of protruded partitions of n with largest part at most 5.
[ "1", "3", "6", "13", "25", "49", "91", "170", "309", "558", "992", "1752", "3062", "5317", "9166", "15712", "26784", "45447", "76775", "129203", "216662", "362177", "603671", "1003566", "1664389", "2754382", "4549207", "7500096", "12344840", "20288723", "33298979", "54584077", "89373081", "146182754" ]
[ "nonn" ]
18
1
2
null
[ "M2569" ]
N. J. A. Sloane.
2025-01-05T19:51:33
oeisdata/seq/A005/A005406.seq
774bdafa60e4bc105debe997aa06aa8c
A005407
Number of protruded partitions of n with largest part at most 6.
[ "1", "3", "6", "13", "25", "50", "93", "175", "320", "582", "1041", "1851", "3253", "5682", "9848", "16970", "29070", "49559", "84090", "142107", "239239", "401404", "671386", "1119799", "1862861", "3091708", "5120090", "8462535", "13961695", "22996307", "37819865", "62112581", "101879568", "166912537", "273166466", "446623176" ]
[ "nonn" ]
26
1
2
null
[ "M2570" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A005/A005407.seq
4f7c6627ba82a5d01093333d4d3b78c4
A005408
The odd numbers: a(n) = 2*n + 1.
[ "1", "3", "5", "7", "9", "11", "13", "15", "17", "19", "21", "23", "25", "27", "29", "31", "33", "35", "37", "39", "41", "43", "45", "47", "49", "51", "53", "55", "57", "59", "61", "63", "65", "67", "69", "71", "73", "75", "77", "79", "81", "83", "85", "87", "89", "91", "93", "95", "97", "99", "101", "103", "105", "107", "109", "111", "113", "115", "117", "119", "121", "123", "125", "127", "129", "131" ]
[ "nonn", "core", "nice", "easy" ]
468
0
2
[ "A000027", "A000290", "A000754", "A001651", "A003558", "A005408", "A005843", "A047209", "A065091", "A078050", "A109613", "A120062", "A128200", "A144106", "A167875", "A179480", "A216371" ]
[ "M2400" ]
N. J. A. Sloane
2025-03-15T14:46:27
oeisdata/seq/A005/A005408.seq
a41e4a40bac2ecb889ece0510263782c
A005409
Number of polynomials of height n: a(1)=1, a(2)=1, a(3)=4, a(n) = 2*a(n-1) + a(n-2) + 2 for n >= 4.
[ "1", "1", "4", "11", "28", "69", "168", "407", "984", "2377", "5740", "13859", "33460", "80781", "195024", "470831", "1136688", "2744209", "6625108", "15994427", "38613964", "93222357", "225058680", "543339719", "1311738120", "3166815961", "7645370044", "18457556051", "44560482148", "107578520349", "259717522848" ]
[ "nonn", "easy", "nice" ]
142
1
3
[ "A000129", "A001333", "A005409", "A006189", "A048654", "A048655", "A048745", "A214931", "A216211" ]
[ "M3418" ]
N. J. A. Sloane, S. M. Diano
2025-02-21T12:31:45
oeisdata/seq/A005/A005409.seq
02d783664c3cfcf0be9f1758e2ab1f73
A005410
a(n) = largest integer m such that every n-point interval order contains an m-point semiorder.
[ "1", "2", "3", "3", "4", "4", "5", "5", "6", "6", "7", "7", "8", "8", "9", "9", "9", "10" ]
[ "nonn", "more" ]
25
1
2
null
[ "M0435" ]
N. J. A. Sloane.
2017-07-01T02:18:14
oeisdata/seq/A005/A005410.seq
041b2b9bf566699cd785e85489f084bf
A005411
Number of non-vanishing Feynman diagrams of order 2n for the electron or the photon propagators in quantum electrodynamics.
[ "1", "1", "4", "25", "208", "2146", "26368", "375733", "6092032", "110769550", "2232792064", "49426061818", "1192151302144", "31123028996164", "874428204384256", "26308967412122125", "843984969276915712", "28757604639850111894", "1037239628039528906752", "39481325230750749160462" ]
[ "nonn", "easy" ]
170
0
3
[ "A000108", "A000698", "A005411", "A005412", "A005413", "A094664", "A258219", "A258220" ]
[ "M3610" ]
N. J. A. Sloane
2023-08-30T09:19:42
oeisdata/seq/A005/A005411.seq
96784a03274134a8a2bd0eb2944179e4
A005412
Number of non-vanishing Feynman diagrams of order 2n for the vacuum polarization (the proper two-point function of the photon) and for the self-energy (the proper two-point function of the electron) in quantum electrodynamics (QED).
[ "1", "3", "18", "153", "1638", "20898", "307908", "5134293", "95518278", "1961333838", "44069970348", "1075902476058", "28367410077468", "803551902237828", "24342558819042888", "785445178323709773", "26896354975287884358", "974297972094661642518", "37225733779871789177628", "1496237868417003741147438" ]
[ "nonn", "easy" ]
92
1
2
[ "A005411", "A005412", "A258219" ]
[ "M3050" ]
N. J. A. Sloane
2024-08-02T01:58:32
oeisdata/seq/A005/A005412.seq
07d0bdb757ff7e31c9329aed8ae9e792
A005413
Number of non-vanishing Feynman diagrams of order 2n+1 for the electron-electron-photon proper vertex function in quantum electrodynamics (QED).
[ "1", "1", "7", "72", "891", "12672", "202770", "3602880", "70425747", "1503484416", "34845294582", "872193147840", "23469399408510", "676090493459712", "20771911997290116", "678287622406488192", "23466105907996232835", "857623856612704266240" ]
[ "nonn", "easy" ]
78
0
3
[ "A000698", "A005411", "A005413" ]
[ "M4445" ]
N. J. A. Sloane
2023-03-05T03:12:26
oeisdata/seq/A005/A005413.seq
c48c9573c741f3a0d7ae79e5d54cccd0
A005414
Feynman diagrams of order 2n with vertex skeletons.
[ "1", "1", "13", "93", "1245", "18093", "308605", "5887453", "124221373", "2864305277", "71589605885", "1927010749181", "55572839581437", "1709604517055229", "55893262628149245", "1935654236127347709", "70799043456576835581", "2727771901780930132989", "110438840436968476274685", "4688223534904569925386237" ]
[ "nonn" ]
40
1
3
[ "A000698", "A001147", "A005411", "A005412", "A005413", "A005414", "A005416", "A049464" ]
[ "M4906" ]
N. J. A. Sloane.
2018-10-05T04:16:21
oeisdata/seq/A005/A005414.seq
9ea55104f3e0bc7e914fff971b3b9764
A005415
Number of simple tensors with n external gluons.
[ "1", "0", "1", "2", "15", "140", "1915", "33810", "734545", "18929960", "564216345", "19088149850", "722508543295", "30249199720740", "1387823333771875", "69238799231051450", "3731906171773805025", "216101966957781304400", "13379538319131196637425", "881962125004262056604850" ]
[ "nonn", "nice" ]
34
0
4
[ "A001813", "A005415" ]
[ "M2080" ]
N. J. A. Sloane
2022-11-21T03:50:52
oeisdata/seq/A005/A005415.seq
e9f91aaeff104d2a821a471c51d5f15e
A005416
Vertex diagrams of order 2n.
[ "1", "1", "6", "50", "518", "6354", "89782", "1435330", "25625910", "505785122", "10944711398", "257834384850", "6572585595622", "180334118225650", "5300553714899094", "166206234856979810", "5538980473666776854", "195527829569946627138", "7288988096561232432070" ]
[ "nonn", "nice", "easy" ]
38
0
3
[ "A000698", "A001147", "A005416", "A049464" ]
[ "M4259" ]
N. J. A. Sloane
2022-01-31T06:48:00
oeisdata/seq/A005/A005416.seq
4109f5ee66fa3c122e8328fdda7e3efb
A005417
Maximal period of an n-stage shift register.
[ "2", "6", "12", "30", "60", "120", "210", "420", "840", "1260", "2520", "2520", "5040", "9240", "13860", "27720", "32760", "55440", "65520", "120120", "180180", "360360", "360360", "720720", "720720", "942480", "1113840" ]
[ "nonn", "nice", "more" ]
34
0
1
[ "A000793", "A005417", "A080742", "A080743" ]
[ "M1587" ]
N. J. A. Sloane
2023-10-01T22:38:36
oeisdata/seq/A005/A005417.seq
0b2562a35f0f97105d935a08fcfa26e4
A005418
Number of (n-1)-bead black-white reversible strings; also binary grids; also row sums of Losanitsch's triangle A034851; also number of caterpillar graphs on n+2 vertices.
[ "1", "2", "3", "6", "10", "20", "36", "72", "136", "272", "528", "1056", "2080", "4160", "8256", "16512", "32896", "65792", "131328", "262656", "524800", "1049600", "2098176", "4196352", "8390656", "16781312", "33558528", "67117056", "134225920", "268451840", "536887296", "1073774592", "2147516416", "4295032832" ]
[ "nonn", "easy", "nice", "changed" ]
335
1
2
[ "A000079", "A001444", "A001445", "A001998", "A005418", "A007582", "A016116", "A032085", "A051436", "A051437", "A060546", "A122746", "A131577", "A277504", "A320750" ]
[ "M0771" ]
N. J. A. Sloane, R. K. Guy
2025-04-21T02:30:11
oeisdata/seq/A005/A005418.seq
a8d65e214ebfe4537dfb46d52af56438
A005419
Number of nonequivalent dissections of a polygon into n heptagons by nonintersecting diagonals up to rotation and reflection.
[ "1", "1", "3", "16", "112", "1020", "10222", "109947", "1230840", "14218671", "168256840", "2031152928", "24931793768", "310420597116", "3912823963482", "49853370677834", "641218583442360", "8316918403772790", "108686334145327785", "1429927553582849256", "18927697628428129728", "251931892228273729375" ]
[ "nonn" ]
27
1
3
[ "A005419", "A295260" ]
[ "M3023" ]
N. J. A. Sloane
2017-11-20T22:06:32
oeisdata/seq/A005/A005419.seq
699490f8c1dc5c47091af90de566d74c
A005420
Largest prime factor of 2^n - 1.
[ "3", "7", "5", "31", "7", "127", "17", "73", "31", "89", "13", "8191", "127", "151", "257", "131071", "73", "524287", "41", "337", "683", "178481", "241", "1801", "8191", "262657", "127", "2089", "331", "2147483647", "65537", "599479", "131071", "122921", "109", "616318177", "524287", "121369", "61681", "164511353", "5419" ]
[ "nonn" ]
101
2
1
[ "A000043", "A000225", "A002326", "A002587", "A005420", "A006530", "A274906", "A337431", "A359063", "A359088" ]
[ "M2609" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005420.seq
67e68321411693f84d75d5b0a1bd3a90
A005421
Number of numbers of complexity n, i.e., that can be built from n ones using + and *, and require at least that many ones.
[ "1", "1", "1", "1", "2", "3", "2", "6", "6", "7", "14", "16", "20", "34", "42", "56", "84", "108", "152", "214", "295", "398", "569", "763", "1094", "1475", "2058", "2878", "3929", "5493", "7669", "10501", "14707", "20476", "28226", "39287", "54817", "75619", "105584", "146910", "203294", "283764", "394437", "547485", "763821", "1061367", "1476067", "2057708", "2861449" ]
[ "nonn", "nice" ]
43
1
5
[ "A005245", "A005421", "A005520" ]
[ "M0430" ]
Simon Plouffe
2025-02-16T08:32:28
oeisdata/seq/A005/A005421.seq
3884c4ae54a8c6bb30b79ca38a312189
A005422
Largest prime factor of 10^n - 1.
[ "3", "11", "37", "101", "271", "37", "4649", "137", "333667", "9091", "513239", "9901", "265371653", "909091", "2906161", "5882353", "5363222357", "333667", "1111111111111111111", "27961", "10838689", "513239", "11111111111111111111111", "99990001", "182521213001", "1058313049" ]
[ "nonn" ]
50
1
1
[ "A002275", "A002283", "A003020", "A004023", "A005422", "A006530", "A067063", "A075024", "A102380", "A274906" ]
[ "M2889" ]
N. J. A. Sloane
2024-08-02T12:04:21
oeisdata/seq/A005/A005422.seq
57be1e8f3742a024ccf4b37c619f52ae
A005423
A finite sequence associated with the Lie algebra A_6.
[ "1", "2", "3", "4", "5", "6", "8", "10", "11", "14", "20", "21", "35", "56" ]
[ "nonn", "fini", "full" ]
5
0
2
null
null
N. J. A. Sloane.
2012-03-30T16:44:45
oeisdata/seq/A005/A005423.seq
2f9f68a6768f4fe404694da67902c31c
A005424
Smallest number that requires n iterations of the bi-unitary totient function (A116550) to reach 1.
[ "2", "3", "4", "5", "8", "9", "13", "16", "17", "24", "25", "35", "44", "63", "64", "91", "97", "128", "193", "221", "259", "324", "353", "391", "477", "702", "929", "1188", "1269", "1589", "1613", "2017", "2309", "2623", "3397", "4064", "4781", "5468", "6515", "6887", "9213", "12286", "12887", "14009", "16564", "16897", "17803", "30428", "36256" ]
[ "nonn", "nice" ]
39
1
1
[ "A005424", "A116550", "A225175", "A225176" ]
[ "M0530" ]
N. J. A. Sloane
2022-07-16T07:09:38
oeisdata/seq/A005/A005424.seq
4b1be1485b717744f4e4d982151436d7
A005425
a(n) = 2*a(n-1) + (n-1)*a(n-2).
[ "1", "2", "5", "14", "43", "142", "499", "1850", "7193", "29186", "123109", "538078", "2430355", "11317646", "54229907", "266906858", "1347262321", "6965034370", "36833528197", "199037675054", "1097912385851", "6176578272782", "35409316648435", "206703355298074", "1227820993510153", "7416522514174082" ]
[ "nonn", "easy", "nice" ]
178
0
2
[ "A002872", "A005425", "A080337", "A085483", "A093620", "A100510", "A100862", "A111062", "A128227", "A344678" ]
[ "M1461" ]
Simon Plouffe
2024-01-25T08:36:39
oeisdata/seq/A005/A005425.seq
b9e7904007f82a6f628e4ba61b4cb910
A005426
Number of linear geometries on n points with <= 3 points per line.
[ "1", "1", "1", "2", "2", "3", "5", "11", "32", "163", "1680" ]
[ "nonn", "hard", "nice" ]
20
0
4
null
[ "M0292" ]
N. J. A. Sloane, Simon Plouffe
2023-09-06T22:43:43
oeisdata/seq/A005/A005426.seq
782d9a43c95cbdb12a9cf595dbfc72f7
A005427
Josephus problem: numbers m such that, when m people are arranged on a circle and numbered 1 through m, the final survivor when we remove every 4th person is one of the first three people.
[ "5", "7", "9", "12", "16", "22", "29", "39", "52", "69", "92", "123", "164", "218", "291", "388", "517", "690", "920", "1226", "1635", "2180", "2907", "3876", "5168", "6890", "9187", "12249", "16332", "21776", "29035", "38713", "51618", "68824", "91765", "122353", "163138", "217517", "290023", "386697", "515596", "687461", "916615", "1222153", "1629538", "2172717", "2896956", "3862608", "5150144", "6866859", "9155812", "12207749", "16276999", "21702665", "28936887", "38582516", "51443354" ]
[ "nonn" ]
118
1
1
[ "A005427", "A005428", "A011782", "A072493", "A073941", "A120160", "A120170", "A120178", "A120186", "A120194", "A120202" ]
[ "M3759" ]
N. J. A. Sloane, Simon Plouffe
2024-08-06T06:40:54
oeisdata/seq/A005/A005427.seq
c05e210cc8d8c089477076ed0d53e288
A005428
a(n) = ceiling((1 + sum of preceding terms) / 2) starting with a(0) = 1.
[ "1", "1", "2", "3", "4", "6", "9", "14", "21", "31", "47", "70", "105", "158", "237", "355", "533", "799", "1199", "1798", "2697", "4046", "6069", "9103", "13655", "20482", "30723", "46085", "69127", "103691", "155536", "233304", "349956", "524934", "787401", "1181102", "1771653", "2657479", "3986219", "5979328", "8968992", "13453488", "20180232", "30270348", "45405522", "68108283", "102162425", "153243637", "229865456", "344798184" ]
[ "nonn", "easy", "nice" ]
112
0
3
[ "A000079", "A005427", "A005428", "A006999", "A024629", "A061418", "A061419", "A072493", "A073941", "A081614", "A081615", "A082125", "A082416", "A120160", "A120170", "A120178", "A120186", "A120194", "A120202" ]
[ "M0572" ]
N. J. A. Sloane and Simon Plouffe
2025-02-16T08:32:28
oeisdata/seq/A005/A005428.seq
11bb6b8286a3c641cb8de0bc68936b78
A005429
Apéry numbers: n^3*C(2n,n).
[ "0", "2", "48", "540", "4480", "31500", "199584", "1177176", "6589440", "35443980", "184756000", "938929992", "4672781568", "22850118200", "110079950400", "523521630000", "2462025277440", "11465007358860", "52926189069600", "242433164404200", "1102772230560000", "4984806175188840", "22404445765690560" ]
[ "nonn", "nice", "easy" ]
51
0
2
[ "A002736", "A005258", "A005259", "A005429", "A005430", "A145438" ]
[ "M2169" ]
Simon Plouffe
2022-11-20T08:35:13
oeisdata/seq/A005/A005429.seq
5f6520656d46ffbf256a201cbfb241aa
A005430
Apéry numbers: n*C(2*n,n).
[ "0", "2", "12", "60", "280", "1260", "5544", "24024", "102960", "437580", "1847560", "7759752", "32449872", "135207800", "561632400", "2326762800", "9617286240", "39671305740", "163352435400", "671560012200", "2756930576400", "11303415363240", "46290177201840", "189368906734800", "773942488394400" ]
[ "nonn", "easy", "nice" ]
126
0
2
[ "A001803", "A002011", "A002457", "A002736", "A003506", "A005258", "A005259", "A005429", "A005430", "A061928" ]
[ "M2028" ]
Simon Plouffe
2025-01-05T19:51:33
oeisdata/seq/A005/A005430.seq
c0c62a151591d03b11a24372f120e8ff
A005431
Embeddings of n-bouquet in sphere.
[ "1", "1", "4", "40", "672", "16128", "506880", "19768320", "922521600", "50185175040", "3120605429760", "218442380083200", "17004899126476800", "1457562782269440000", "136427876420419584000", "13847429456672587776000" ]
[ "easy", "nonn", "nice" ]
41
0
3
[ "A005431", "A123828", "A128850" ]
[ "M3674" ]
Simon Plouffe and N. J. A. Sloane
2025-01-23T16:29:34
oeisdata/seq/A005/A005431.seq
db9aaccdc6e64d4e61dcc99496bfca0a
A005432
Number of permutation groups of degree n (or, number of distinct subgroups of symmetric group S_n, counting conjugates as distinct).
[ "1", "1", "2", "6", "30", "156", "1455", "11300", "151221", "1694723", "29594446", "404126228", "10594925360", "175238308453", "5651774693595", "117053117995400", "5320744503742316", "125889331236297288", "7598016157515302757" ]
[ "nonn", "hard", "more", "nice" ]
62
0
3
[ "A000001", "A000019", "A000638", "A005432" ]
[ "M1690" ]
N. J. A. Sloane, Simon Plouffe
2023-12-22T12:10:43
oeisdata/seq/A005/A005432.seq
fcc4abdddf5de73f4aece11fbeba0f5e
A005433
A finite sequence associated with the Lie algebra B_3.
[ "1", "2", "3", "4", "10", "28" ]
[ "nonn", "fini", "full" ]
5
0
2
null
null
N. J. A. Sloane.
2012-03-30T16:44:45
oeisdata/seq/A005/A005433.seq
bbfe4ff8dcf73de99bef617fb41784b5
A005434
Number of distinct autocorrelations of binary words of length n.
[ "1", "2", "3", "4", "6", "8", "10", "13", "17", "21", "27", "30", "37", "47", "57", "62", "75", "87", "102", "116", "135", "155", "180", "194", "220", "254", "289", "312", "359", "392", "438", "479", "538", "595", "664", "701", "772", "863", "956", "1005", "1115", "1205", "1317", "1414", "1552", "1677", "1836", "1920", "2074", "2249", "2444" ]
[ "nonn", "nice" ]
70
1
2
[ "A005434", "A018819", "A045690" ]
[ "M0555" ]
Simon Plouffe, N. J. A. Sloane
2024-10-21T13:15:04
oeisdata/seq/A005/A005434.seq
b9f17f1152fd699e9b7f05c19bbd3f8e
A005435
Number of column-convex polyominoes with perimeter 2n+2.
[ "1", "2", "7", "28", "122", "558", "2641", "12822", "63501", "319554", "1629321", "8399092", "43701735", "229211236", "1210561517", "6432491192", "34364148528", "184463064936", "994430028087", "5381653402890", "29226425965907", "159227245772460", "870004781620093", "4766330416567254", "26176585256712224" ]
[ "nonn", "nice" ]
34
1
2
[ "A005435", "A006027", "A269228" ]
[ "M1779" ]
Simon Plouffe
2021-03-28T01:40:27
oeisdata/seq/A005/A005435.seq
52c854959b5f5367580f49a591fbbd74
A005436
Number of convex polygons of perimeter 2n on square lattice.
[ "1", "2", "7", "28", "120", "528", "2344", "10416", "46160", "203680", "894312", "3907056", "16986352", "73512288", "316786960", "1359763168", "5815457184", "24788842304", "105340982248", "446389242480", "1886695382192", "7955156287456", "33468262290096", "140516110684832", "588832418973280", "2463133441338048" ]
[ "nonn" ]
96
2
2
[ "A005436", "A005768", "A005769", "A005770", "A093118", "A260346", "A324009" ]
[ "M1778" ]
Simon Plouffe and N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005436.seq
189ba0b6c2e45cb6968adef2d06e6a3b
A005437
Column of Kempner tableau.
[ "1", "1", "1", "2", "4", "14", "46", "224", "1024", "6320", "36976", "275792", "1965664", "17180144", "144361456", "1446351104", "13997185024", "158116017920", "1731678144256", "21771730437632", "266182076161024", "3686171162253824", "49763143319190016", "752594181757712384", "11118629668610842624" ]
[ "nonn" ]
43
0
4
[ "A005437", "A008281", "A008282", "A010094", "A064192", "A108040" ]
[ "M1276" ]
Simon Plouffe
2023-04-28T12:09:44
oeisdata/seq/A005/A005437.seq
68f4c1e06db6dc3341e8b5cb4ff62ddf
A005438
Column of Kempner tableau.
[ "1", "1", "5", "10", "56", "178", "1202", "5296", "42272", "238816", "2204480", "15214480", "159575936", "1301989648", "15299174672", "144118832896", "1875796977152", "20040052293376", "286222128454400", "3419989086092800", "53183132405282816", "702831038438522368" ]
[ "nonn" ]
17
1
3
[ "A005437", "A005438" ]
[ "M3805" ]
Simon Plouffe
2018-10-15T05:20:19
oeisdata/seq/A005/A005438.seq
cf9556a32d2feaaa363395afd8543685
A005439
Genocchi medians (or Genocchi numbers of second kind).
[ "1", "1", "2", "8", "56", "608", "9440", "198272", "5410688", "186043904", "7867739648", "401293838336", "24290513745920", "1721379917619200", "141174819474169856", "13266093250285568000", "1415974941618255921152", "170361620874699124637696", "22948071824232932086513664", "3439933090471867097102680064" ]
[ "nonn", "nice", "easy", "changed" ]
264
0
3
[ "A000366", "A005439", "A036968", "A110501", "A297703" ]
[ "M1888" ]
Simon Plouffe
2025-04-27T15:03:00
oeisdata/seq/A005/A005439.seq
37977b790a99cf305fae6857d14fddb6
A005440
Coefficients of Gandhi polynomials.
[ "2", "8", "54", "556", "8146", "161424", "4163438", "135634292", "5448798090", "264689281240", "15296907175462", "1037373202178748", "81588771795362114", "7366855482991121696", "756909709680583939806", "87807399365909591247364" ]
[ "nonn", "easy" ]
27
2
1
[ "A005440", "A036970" ]
[ "M1887" ]
N. J. A. Sloane, Simon Plouffe
2017-10-16T20:19:05
oeisdata/seq/A005/A005440.seq
b507c112d5a773372120f65c9f67bd23
A005441
Number of isonemal fabrics of period exactly n.
[ "1", "1", "4", "4", "9", "8", "55", "21", "104", "62", "429", "196", "800", "698", "4674", "2070", "7721", "7154" ]
[ "nonn", "more" ]
34
2
3
[ "A000046", "A005441", "A193140", "A262589" ]
[ "M3230" ]
Simon Plouffe
2023-04-14T10:52:58
oeisdata/seq/A005/A005441.seq
cc8d361fb7632624b343fdb0c4019615
A005442
a(n) = n!*Fibonacci(n+1).
[ "1", "1", "4", "18", "120", "960", "9360", "105840", "1370880", "19958400", "322963200", "5748019200", "111607372800", "2347586841600", "53178757632000", "1290674601216000", "33413695451136000", "919096314200064000", "26768324463648768000" ]
[ "nonn", "easy" ]
73
0
3
[ "A000045", "A000142", "A005442", "A039692", "A039948", "A052585", "A080599" ]
[ "M3549" ]
Simon Plouffe
2025-01-05T19:51:33
oeisdata/seq/A005/A005442.seq
845a3fe5e19c5bfaa7f3cce5f4322bfa
A005443
a(n) = n! * Fibonacci(n).
[ "0", "1", "2", "12", "72", "600", "5760", "65520", "846720", "12337920", "199584000", "3552595200", "68976230400", "1450895846400", "32866215782400", "797681364480000", "20650793619456000", "568032822669312000", "16543733655601152000", "508598164809326592000", "16458582085314969600000" ]
[ "nonn", "easy" ]
46
0
3
[ "A000045", "A000142", "A005442", "A005443", "A039948" ]
[ "M2034" ]
Simon Plouffe
2025-01-05T19:51:33
oeisdata/seq/A005/A005443.seq
b3b0daa039bdd25d0710f45fe1f65434
A005444
From a Fibonacci-like differential equation.
[ "1", "1", "3", "8", "50", "214", "2086", "11976", "162816", "1143576", "20472504", "165910128", "3785092032", "33908109936", "967508478192", "9252123203712", "327062428940160", "3236057604910080", "141403289873955840", "1404243298160352000", "76168955916831029760", "735206146073008508160" ]
[ "sign", "easy" ]
34
0
3
[ "A000045", "A000142", "A005444", "A005445", "A048994" ]
[ "M2766" ]
Simon Plouffe, N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A005/A005444.seq
fe348bdcc169eb11a9613aaeadec3218
A005445
From a Fibonacci-like differential equation.
[ "0", "1", "1", "8", "16", "224", "608", "13320", "41760", "1366152", "4440312", "215100192", "655723440", "48242081328", "121651212720", "14627299801728", "24367884018048", "5768946415383552", "2780730890516736", "2872938805170308352", "-2941729703083507968", "1764460446550873413120" ]
[ "sign" ]
33
0
4
[ "A000045", "A000142", "A005444", "A005445", "A048994", "A320352" ]
[ "M4487" ]
Simon Plouffe
2025-01-05T19:51:33
oeisdata/seq/A005/A005445.seq
38e9331def1163cedbfe0ff94b77c34c
A005446
Denominators of expansion of -W_{-1}(-e^{-1-x^2/2}) where W_{-1} is Lambert W function.
[ "1", "1", "3", "36", "270", "4320", "17010", "5443200", "204120", "2351462400", "1515591000", "2172751257600", "354648294000", "10168475885568000", "7447614174000", "1830325659402240000", "1595278956070800000", "2987091476144455680000" ]
[ "nonn", "frac" ]
50
0
3
[ "A005446", "A005447", "A065973", "A090804", "A299430", "A299431", "A299432", "A299433" ]
[ "M3140" ]
N. J. A. Sloane
2022-11-22T02:32:33
oeisdata/seq/A005/A005446.seq
fcda55acc268272ee394e4a7a0a4350b
A005447
Numerators of the expansion of -W_{-1}(-e^(-1 - x^2/2)) where x > 0 and W_{-1} is the Lambert W function.
[ "1", "1", "1", "1", "-1", "1", "1", "-139", "1", "-571", "-281", "163879", "-5221", "5246819", "5459", "-534703531", "91207079", "-4483131259", "-2650986803", "432261921612371", "-6171801683", "6232523202521089", "4283933145517", "-25834629665134204969", "11963983648109" ]
[ "sign", "frac" ]
61
0
8
[ "A005446", "A005447", "A065973", "A090804", "A299430", "A299431", "A299432", "A299433" ]
[ "M5399" ]
N. J. A. Sloane
2022-11-22T02:37:06
oeisdata/seq/A005/A005447.seq
bc51f5e12c5c52b5fda40d34bdf0a605
A005448
Centered triangular numbers: a(n) = 3*n*(n-1)/2 + 1.
[ "1", "4", "10", "19", "31", "46", "64", "85", "109", "136", "166", "199", "235", "274", "316", "361", "409", "460", "514", "571", "631", "694", "760", "829", "901", "976", "1054", "1135", "1219", "1306", "1396", "1489", "1585", "1684", "1786", "1891", "1999", "2110", "2224", "2341", "2461", "2584", "2710", "2839", "2971", "3106", "3244", "3385", "3529" ]
[ "nonn", "easy", "nice" ]
258
1
2
[ "A000217", "A000292", "A001263", "A001844", "A002061", "A003154", "A005448", "A006003", "A008486", "A008585", "A045943", "A134482", "A146325", "A226903", "A242357", "A255437" ]
[ "M3378" ]
N. J. A. Sloane, R. K. Guy, Dec 12 1974
2025-02-16T08:32:28
oeisdata/seq/A005/A005448.seq
48abd0dd9b97feec548cd10a5d900d48
A005449
Second pentagonal numbers: a(n) = n*(3*n + 1)/2.
[ "0", "2", "7", "15", "26", "40", "57", "77", "100", "126", "155", "187", "222", "260", "301", "345", "392", "442", "495", "551", "610", "672", "737", "805", "876", "950", "1027", "1107", "1190", "1276", "1365", "1457", "1552", "1650", "1751", "1855", "1962", "2072", "2185", "2301", "2420", "2542", "2667", "2795", "2926", "3060", "3197", "3337", "3480" ]
[ "nonn", "easy" ]
269
0
2
[ "A000217", "A000320", "A000326", "A001318", "A005449", "A006002", "A016789", "A022289", "A033568", "A045943", "A049451", "A059845", "A101165", "A101166", "A115067", "A140090", "A140091", "A140672", "A140675", "A151542", "A226488" ]
null
N. J. A. Sloane
2025-04-02T05:15:42
oeisdata/seq/A005/A005449.seq
80b6b9b094410e163f86f28827cca490
A005450
Numerator of (1 + Gamma(n))/n.
[ "2", "1", "1", "7", "5", "121", "103", "5041", "40321", "362881", "329891", "39916801", "36846277", "6227020801", "87178291201", "1307674368001", "1230752346353", "355687428096001", "336967037143579", "121645100408832001", "2432902008176640001" ]
[ "nonn", "frac" ]
25
1
1
[ "A005450", "A005451" ]
null
N. J. A. Sloane
2022-11-22T21:41:42
oeisdata/seq/A005/A005450.seq
f9ea310d7d4ed867ec5c8a20d411cc31
A005451
a(n)=1 if n is a prime number, otherwise a(n)=n.
[ "1", "1", "1", "4", "1", "6", "1", "8", "9", "10", "1", "12", "1", "14", "15", "16", "1", "18", "1", "20", "21", "22", "1", "24", "25", "26", "27", "28", "1", "30", "1", "32", "33", "34", "35", "36", "1", "38", "39", "40", "1", "42", "1", "44", "45", "46", "1", "48", "49", "50", "51", "52", "1", "54", "55", "56", "57", "58", "1", "60" ]
[ "nonn", "frac" ]
39
1
4
[ "A005450", "A005451", "A088140", "A089026", "A135684", "A181569" ]
null
N. J. A. Sloane
2022-11-23T11:41:47
oeisdata/seq/A005/A005451.seq
c7810ad16a7a1d3642ec69c1ffc2b4fb
A005452
Number of positions that the 3 X 3 X 3 Rubik cube puzzle can be in after exactly n moves, up to equivalence under the full group of order 48 of the cube and with a half-turn is considered to be 2 moves.
[ "1", "1", "5", "25", "219", "1978", "18395", "171529", "1601725", "14956266", "139629194", "1303138445", "12157779067", "113382522382", "1056867697737", "9843661720634", "91532722388023", "846837132071729", "7668156860181597" ]
[ "nonn", "fini" ]
25
0
3
[ "A005452", "A080583", "A080601", "A080602", "A080638" ]
null
N. J. A. Sloane, Feb 25 2003
2025-01-12T17:37:52
oeisdata/seq/A005/A005452.seq
99de359e7a8044f80d8c9e8349b1dcb2
A005453
A finite sequence associated with the Lie algebra B_4.
[ "1", "2", "3", "4", "6", "10", "11", "12", "28", "60" ]
[ "nonn", "fini", "full" ]
7
0
2
null
null
N. J. A. Sloane.
2012-03-30T16:44:45
oeisdata/seq/A005/A005453.seq
52471ad47f2f71c7b878799c2b84450e
A005454
A finite sequence associated with the Lie algebra C_3.
[ "1", "2", "3", "8", "10", "11", "35" ]
[ "nonn", "fini", "full" ]
7
0
2
null
null
N. J. A. Sloane.
2012-03-30T16:44:45
oeisdata/seq/A005/A005454.seq
7d69b465130b1c030e47d58313c55e3a
A005455
A finite sequence associated with the Lie algebra C_4.
[ "1", "2", "3", "4", "8", "9", "10", "11", "12", "20", "35", "36", "84" ]
[ "nonn", "fini", "full" ]
5
0
2
null
null
N. J. A. Sloane.
2012-03-30T16:44:45
oeisdata/seq/A005/A005455.seq
d4d504706a3c544b8168ed53a0b00944
A005456
A finite sequence associated with the Lie algebra D_4.
[ "1", "2", "3", "4", "10", "12", "28" ]
[ "nonn", "fini", "full" ]
5
0
2
null
null
N. J. A. Sloane.
2012-03-30T16:44:45
oeisdata/seq/A005/A005456.seq
6a850492ddadb651e6970fabdd8247c6
A005457
A finite sequence associated with the Lie algebra D_5.
[ "1", "2", "3", "4", "6", "10", "11", "12", "20", "28", "30", "60" ]
[ "nonn", "fini", "full" ]
7
0
2
null
null
N. J. A. Sloane.
2012-03-30T16:44:45
oeisdata/seq/A005/A005457.seq
ab80969e6701039e0e6fad094a420e6c
A005458
A finite sequence associated with the Lie algebra F_4.
[ "1", "2", "3", "4", "6", "8", "9", "10", "11", "12", "28", "35", "36", "60", "156" ]
[ "nonn", "fini", "full" ]
5
0
2
null
null
N. J. A. Sloane.
2012-03-30T16:44:45
oeisdata/seq/A005/A005458.seq
65fd1bbd52c3b8bda3d79c89d814f1fa
A005459
A finite sequence associated with the Lie algebra E_6.
[ "1", "2", "3", "4", "5", "6", "8", "9", "10", "11", "12", "20", "21", "28", "30", "35", "36", "60", "84", "156" ]
[ "nonn", "fini", "full" ]
7
0
2
null
null
N. J. A. Sloane.
2012-03-30T16:44:45
oeisdata/seq/A005/A005459.seq
a1cce98eb199cfa5a088d8907235f54a
A005460
a(n) = (3*n+4)*(n+3)!/24.
[ "1", "7", "50", "390", "3360", "31920", "332640", "3780000", "46569600", "618710400", "8821612800", "134399865600", "2179457280000", "37486665216000", "681734237184000", "13071512982528000", "263564384219136000", "5575400435404800000", "123469776914964480000", "2856835183101419520000" ]
[ "nonn", "easy" ]
44
0
2
[ "A005460", "A028246" ]
[ "M4433" ]
N. J. A. Sloane
2022-11-22T22:18:26
oeisdata/seq/A005/A005460.seq
654b62f72e6c887f5761e21d06d92b72
A005461
Number of simplices in barycentric subdivision of n-simplex.
[ "1", "15", "180", "2100", "25200", "317520", "4233600", "59875200", "898128000", "14270256000", "239740300800", "4249941696000", "79332244992000", "1556132497920000", "32011868528640000", "689322235650048000", "15509750302126080000", "364022962973429760000", "8898339094906060800000" ]
[ "nonn", "easy", "nice" ]
62
1
2
[ "A001113", "A001297", "A001620", "A005460", "A005461", "A005462", "A005463", "A005464", "A005465", "A028246", "A091725", "A099285" ]
[ "M4985" ]
N. J. A. Sloane
2022-11-23T08:57:37
oeisdata/seq/A005/A005461.seq
39b8fbea5bdc6ee06853657c519edb4c
A005462
Number of simplices in barycentric subdivision of n-simplex.
[ "1", "31", "602", "10206", "166824", "2739240", "46070640", "801496080", "14495120640", "273158645760", "5368729766400", "110055327782400", "2351983118284800", "52361635508582400", "1213240925049753600", "29227769646147072000", "731310069474496512000", "18984684514588176384000" ]
[ "nonn", "easy" ]
34
3
2
[ "A001298", "A005460", "A005461", "A005462", "A028246" ]
[ "M5225" ]
N. J. A. Sloane
2022-11-23T08:57:53
oeisdata/seq/A005/A005462.seq
c262429ef0ae05834039a36597d09d9f
A005463
Number of simplices in barycentric subdivision of n-simplex.
[ "1", "63", "1932", "46620", "1020600", "21538440", "451725120", "9574044480", "207048441600", "4595022432000", "105006251750400", "2475732702643200", "60284572969420800", "1516762345722624000", "39433286715863040000", "1059143615076298752000", "29378569022287220736000", "841159994641469927424000" ]
[ "nonn" ]
27
4
2
[ "A005460", "A005461", "A005462", "A005463", "A005464", "A005465", "A028246", "A112494" ]
[ "M5326" ]
N. J. A. Sloane
2022-11-23T08:57:57
oeisdata/seq/A005/A005463.seq
51caa72446512dc3e11be6c4afd54993
A005464
Number of simplices in barycentric subdivision of n-simplex.
[ "1", "127", "6050", "204630", "5921520", "158838240", "4115105280", "105398092800", "2706620716800", "70309810771200", "1858166876966400", "50148628078348800", "1385482985542656000", "39245951652171264000", "1140942623868343296000", "34060437199245929472000", "1044402668566817624064000", "32895725269182358302720000" ]
[ "nonn", "easy" ]
27
5
2
[ "A005460", "A005461", "A005462", "A005463", "A005464", "A005465", "A028246", "A144969" ]
[ "M5391" ]
N. J. A. Sloane
2022-11-23T08:57:50
oeisdata/seq/A005/A005464.seq
9af7317ef5685acb720a1378519fab1f
A005465
Number of n-dimensional hypotheses allowing for conditional independence.
[ "0", "0", "1", "10", "70", "431", "2534", "14820", "88267", "542912", "3475978", "23253693", "162723444", "1190464900", "9092400633", "72370378750", "599168889634", "5150536258735", "45891028609826", "423144495659912", "4031842435506171", "39645279656283820", "401806832058661334", "4192631368792015237", "44992655908959220440" ]
[ "nonn", "nice" ]
68
0
4
[ "A000110", "A005465", "A058681", "A058692" ]
[ "M4725" ]
N. J. A. Sloane
2024-01-15T17:17:31
oeisdata/seq/A005/A005465.seq
50262e900bd8d9b5584b1feba21b697e
A005466
5 X 5 stochastic matrices of integers.
[ "1", "115", "5390", "101275", "858650", "3309025", "4718075" ]
[ "nonn", "fini", "full" ]
20
0
2
[ "A001496", "A005466", "A005467" ]
[ "M5373" ]
N. J. A. Sloane.
2017-07-01T02:18:26
oeisdata/seq/A005/A005466.seq
a616e31e523fb212457fca22446041c2
A005467
6 X 6 stochastic matrices of integers.
[ "1", "714", "196677", "18941310", "809451144", "17914693608", "223688514048", "1633645276848", "6907466271384", "15642484909560", "14666561365176" ]
[ "nonn", "fini", "full" ]
23
0
2
[ "A005466", "A005467" ]
[ "M5470" ]
N. J. A. Sloane
2020-04-09T22:25:15
oeisdata/seq/A005/A005467.seq
94022c68c29ca27fecc1747606f104b7
A005468
a(n) = 1 + a(floor(n/2))*a(ceiling(n/2)).
[ "1", "2", "3", "5", "7", "10", "16", "26", "36", "50", "71", "101", "161", "257", "417", "677", "937", "1297", "1801", "2501", "3551", "5042", "7172", "10202", "16262", "25922", "41378", "66050", "107170", "173890", "282310", "458330", "634350", "877970", "1215290", "1682210", "2335898", "3243602", "4504302", "6255002" ]
[ "nonn", "easy" ]
17
1
2
null
[ "M0649" ]
Colin Mallows
2016-08-17T22:14:42
oeisdata/seq/A005/A005468.seq
02891eb5183dcd1d8fd4fc284fc7b084
A005469
a(n) = 1 + a(floor(n/2))*a(ceiling(n/2)) for n > 1, a(1) = 2.
[ "2", "5", "11", "26", "56", "122", "287", "677", "1457", "3137", "6833", "14885", "35015", "82370", "194300", "458330", "986390", "2122850", "4570610", "9840770", "21435122", "46689890", "101709206", "221563226", "521198276", "1226050226", "2884185551", "6784816901", "16004491001", "37752490001", "89053519001" ]
[ "nonn" ]
21
1
1
[ "A005468", "A005469" ]
[ "M1398" ]
Colin Mallows
2020-11-16T12:10:33
oeisdata/seq/A005/A005469.seq
ea439a010c7f9147cc7d76c9560ff86a
A005470
Number of unlabeled planar simple graphs with n nodes.
[ "1", "1", "2", "4", "11", "33", "142", "822", "6966", "79853", "1140916", "18681008", "333312451" ]
[ "nonn", "core", "nice", "hard", "more" ]
66
0
3
[ "A003094", "A005470", "A034889", "A039735", "A126201" ]
[ "M1252" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005470.seq
2a055004d08f8a166cbbe25a4a50e705
A005471
Primes of the form m^2 + 3m + 9, where m can be positive or negative.
[ "7", "13", "19", "37", "79", "97", "139", "163", "313", "349", "607", "709", "877", "937", "1063", "1129", "1489", "1567", "1987", "2557", "2659", "3313", "3547", "4297", "5119", "5557", "7489", "8017", "8563", "9127", "9319", "9907", "10513", "11779", "12889", "15013", "15259", "16519", "17299", "18097", "18367", "18913", "20029" ]
[ "nonn", "easy" ]
76
1
1
[ "A005471", "A027692", "A175282", "A227622", "A349461" ]
[ "M4345" ]
N. J. A. Sloane
2024-05-14T07:27:04
oeisdata/seq/A005/A005471.seq
5b7a0cb1e7ea2e38be4b90044bdbaa2b
A005472
Class numbers of Shanks' simplest cubic fields.
[ "1", "1", "1", "1", "1", "1", "1", "4", "7", "4", "4", "4", "7", "4", "13", "7", "19", "7", "7", "7", "19", "19", "19", "16", "31", "19", "28", "19", "49", "31", "28", "31", "64", "43", "37", "127", "61", "52", "52", "52", "49", "100", "37", "112", "64", "67", "61", "76", "61", "76", "61", "61", "112", "76", "73", "67", "133", "91", "223", "169", "73", "112", "100", "169", "91", "121", "175" ]
[ "nonn" ]
36
1
8
[ "A003136", "A005471", "A005472", "A005474" ]
[ "M3291" ]
N. J. A. Sloane
2024-12-08T17:27:59
oeisdata/seq/A005/A005472.seq
4e392d01b30db7165c293c39a114b574
A005473
Primes of form k^2 + 4.
[ "5", "13", "29", "53", "173", "229", "293", "733", "1093", "1229", "1373", "2029", "2213", "3253", "4229", "4493", "5333", "7229", "7573", "9029", "9413", "10613", "13229", "13693", "15629", "18229", "18773", "21613", "24029", "26573", "27893", "31333", "33493", "37253", "41213", "42853", "46229", "47093", "54293" ]
[ "nonn", "easy" ]
76
1
1
[ "A000217", "A000290", "A001318", "A001840", "A005473", "A010051", "A016754", "A098062", "A138353", "A146326", "A185086" ]
[ "M3830" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005473.seq
f3297645a9271a1b33ac8ce44c0e7ca5
A005474
Class numbers of the real quadratic fields Q(sqrt(A005473(n))).
[ "1", "1", "1", "1", "1", "3", "1", "3", "5", "3", "3", "7", "3", "5", "7", "3", "3", "5", "9", "7", "3", "5", "5", "15", "9", "19", "5", "13", "9", "9", "5", "19", "9", "5", "7", "15", "13", "9", "9", "15", "25", "13", "9", "27", "19", "15", "21", "7", "13", "11", "23", "9", "13", "13", "11", "33", "15", "25", "23", "15", "13", "29", "21", "17", "43", "35", "27", "33", "17", "17", "27", "45", "11", "63", "15", "31", "17", "15", "33", "15", "31", "31" ]
[ "nonn" ]
21
1
6
[ "A005472", "A005473", "A005474" ]
[ "M2215" ]
N. J. A. Sloane.
2024-12-08T12:44:30
oeisdata/seq/A005/A005474.seq
1bb545c3978102de5fd36a94ee80ba45
A005475
a(n) = n*(5*n+1)/2.
[ "0", "3", "11", "24", "42", "65", "93", "126", "164", "207", "255", "308", "366", "429", "497", "570", "648", "731", "819", "912", "1010", "1113", "1221", "1334", "1452", "1575", "1703", "1836", "1974", "2117", "2265", "2418", "2576", "2739", "2907", "3080", "3258", "3441", "3629" ]
[ "nonn", "easy" ]
68
0
2
[ "A001622", "A005475", "A022289", "A110449", "A130520", "A162147", "A202803" ]
null
N. J. A. Sloane
2022-09-10T07:35:20
oeisdata/seq/A005/A005475.seq
aa84b7fe5ef5b15d81f653d23d6b1050
A005476
a(n) = n*(5*n - 1)/2.
[ "0", "2", "9", "21", "38", "60", "87", "119", "156", "198", "245", "297", "354", "416", "483", "555", "632", "714", "801", "893", "990", "1092", "1199", "1311", "1428", "1550", "1677", "1809", "1946", "2088", "2235", "2387", "2544", "2706", "2873", "3045", "3222", "3404", "3591" ]
[ "nonn", "easy" ]
84
0
2
[ "A000217", "A000290", "A005475", "A005476", "A016754", "A022288", "A033994", "A133694", "A226488", "A294833" ]
null
N. J. A. Sloane
2024-08-02T01:59:10
oeisdata/seq/A005/A005476.seq
2870c4adf752830625e10c8de7f7fff4
A005477
a(n) = 2^(n-1)*(2^n - 1)*Product_{j=1..n-1} (2^j + 1).
[ "0", "1", "18", "420", "16200", "1138320", "152681760", "40012315200", "20727639504000", "21349793828563200", "43852643645542617600", "179883715700853141120000", "1474687052822610564537600000", "24170122236238340825650936320000" ]
[ "nonn" ]
11
0
3
null
null
N. J. A. Sloane
2022-11-26T02:43:44
oeisdata/seq/A005/A005477.seq
7d67b7c6ad3356edc3d9a8608260b8aa
A005478
Prime Fibonacci numbers.
[ "2", "3", "5", "13", "89", "233", "1597", "28657", "514229", "433494437", "2971215073", "99194853094755497", "1066340417491710595814572169", "19134702400093278081449423917", "475420437734698220747368027166749382927701417016557193662268716376935476241" ]
[ "nonn", "nice", "easy" ]
90
1
1
[ "A000045", "A001605", "A005478", "A030426", "A075736", "A099000", "A178762", "A263880", "A303216" ]
[ "M0741" ]
N. J. A. Sloane
2025-03-11T08:42:57
oeisdata/seq/A005/A005478.seq
cb88c29cd611343e07ecb0a63c1ab8e1
A005479
Prime Lucas numbers (cf. A000032).
[ "2", "3", "7", "11", "29", "47", "199", "521", "2207", "3571", "9349", "3010349", "54018521", "370248451", "6643838879", "119218851371", "5600748293801", "688846502588399", "32361122672259149", "412670427844921037470771", "258899611203303418721656157249445530046830073044201152332257717521" ]
[ "nonn", "nice" ]
64
1
1
[ "A000032", "A001606", "A005479", "A113188", "A113192" ]
[ "M2627" ]
N. J. A. Sloane
2025-02-16T08:32:28
oeisdata/seq/A005/A005479.seq
3a8aa552786b5b550b7e2b721384f1f0
A005480
Decimal expansion of cube root of 4.
[ "1", "5", "8", "7", "4", "0", "1", "0", "5", "1", "9", "6", "8", "1", "9", "9", "4", "7", "4", "7", "5", "1", "7", "0", "5", "6", "3", "9", "2", "7", "2", "3", "0", "8", "2", "6", "0", "3", "9", "1", "4", "9", "3", "3", "2", "7", "8", "9", "9", "8", "5", "3", "0", "0", "9", "8", "0", "8", "2", "8", "5", "7", "6", "1", "8", "2", "5", "2", "1", "6", "5", "0", "5", "6", "2", "4", "2", "1", "9", "1", "7", "3", "2", "7", "3", "5", "4", "4", "2", "1", "3", "2", "6", "2", "2", "2", "0", "9", "5", "7", "0", "2", "2", "9", "3", "4", "7", "6" ]
[ "nonn", "cons", "easy" ]
60
1
2
[ "A002580", "A002947", "A005480" ]
[ "M3771" ]
N. J. A. Sloane; entry revised Apr 23 2006
2023-08-21T10:11:26
oeisdata/seq/A005/A005480.seq
133c03db03afdd8c099af8a7ea8dd62c
A005481
Decimal expansion of cube root of 5.
[ "1", "7", "0", "9", "9", "7", "5", "9", "4", "6", "6", "7", "6", "6", "9", "6", "9", "8", "9", "3", "5", "3", "1", "0", "8", "8", "7", "2", "5", "4", "3", "8", "6", "0", "1", "0", "9", "8", "6", "8", "0", "5", "5", "1", "1", "0", "5", "4", "3", "0", "5", "4", "9", "2", "4", "3", "8", "2", "8", "6", "1", "7", "0", "7", "4", "4", "4", "2", "9", "5", "9", "2", "0", "5", "0", "4", "1", "7", "3", "2", "1", "6", "2", "5", "7", "1", "8", "7", "0", "1", "0", "0", "2", "0", "1", "8", "9", "0", "0", "2", "2", "0", "4", "5", "0" ]
[ "nonn", "cons" ]
38
1
2
[ "A002948", "A005481" ]
[ "M4319" ]
N. J. A. Sloane
2025-02-11T14:41:57
oeisdata/seq/A005/A005481.seq
6d19eab94e301468a3fc4f442fee8611
A005482
Decimal expansion of cube root of 7.
[ "1", "9", "1", "2", "9", "3", "1", "1", "8", "2", "7", "7", "2", "3", "8", "9", "1", "0", "1", "1", "9", "9", "1", "1", "6", "8", "3", "9", "5", "4", "8", "7", "6", "0", "2", "8", "2", "8", "6", "2", "4", "3", "9", "0", "5", "0", "3", "4", "5", "8", "7", "5", "7", "6", "6", "2", "1", "0", "6", "4", "7", "6", "4", "0", "4", "4", "7", "2", "3", "4", "2", "7", "6", "1", "7", "9", "2", "3", "0", "7", "5", "6", "0", "0", "7", "5", "2", "5", "4", "4", "1", "4", "7", "7", "2", "8", "5", "7", "0", "9", "9", "0", "4", "5", "4" ]
[ "nonn", "cons", "easy" ]
34
1
2
[ "A005482", "A005483" ]
[ "M4592" ]
N. J. A. Sloane
2025-02-11T10:00:59
oeisdata/seq/A005/A005482.seq
ce35dfd3c61a583a267b36c4adf5c814
A005483
Continued fraction for cube root of 7.
[ "1", "1", "10", "2", "16", "2", "1", "4", "2", "1", "21", "1", "3", "5", "1", "2", "1", "1", "2", "11", "5", "1", "3", "1", "2", "27", "4", "1", "282", "8", "1", "2", "1", "1", "3", "1", "3", "2", "6", "4", "1", "2", "1", "5", "1", "1", "2", "1", "1", "1", "3", "2", "8", "1", "2", "2", "4", "5", "1", "1", "36", "1", "1", "1", "1", "2", "1", "2", "31", "2", "1", "1", "7", "1", "1", "1", "1", "6", "7", "6", "5", "7", "1", "6", "1" ]
[ "nonn", "cofr" ]
25
0
3
[ "A005482", "A005483", "A005484", "A005485" ]
[ "M4675" ]
N. J. A. Sloane
2024-07-05T10:07:17
oeisdata/seq/A005/A005483.seq
0a4ef1eb3a78f50413985e2b98de2c24
A005484
Numerators of continued fraction convergents to cube root of 7.
[ "1", "2", "21", "44", "725", "1494", "2219", "10370", "22959", "33329", "722868", "756197", "2991459", "15713492", "18704951", "53123394", "71828345", "124951739", "321731823", "3664001792", "18641740783", "22305742575", "85558968508", "107864711083", "301288390674", "8242651259281", "33271893427798", "41514544687079" ]
[ "nonn", "frac" ]
25
0
2
[ "A005482", "A005483", "A005484", "A005485" ]
[ "M2127" ]
N. J. A. Sloane, Herman P. Robinson
2024-07-05T10:07:14
oeisdata/seq/A005/A005484.seq
9c3c4f1c5da8c88e97bd368175a1e03e
A005485
Denominators of continued fraction convergents to cube root of 7.
[ "1", "1", "11", "23", "379", "781", "1160", "5421", "12002", "17423", "377885", "395308", "1563809", "8214353", "9778162", "27770677", "37548839", "65319516", "168187871", "1915386097", "9745118356", "11660504453", "44726631715", "56387136168", "157500904051", "4308911545545", "17393147086231", "21702058631776" ]
[ "nonn", "frac" ]
22
0
3
[ "A005482", "A005484", "A005485" ]
[ "M4781" ]
N. J. A. Sloane
2024-07-05T10:07:09
oeisdata/seq/A005/A005485.seq
302879c03c155cb8d76b16ab37793ed7
A005486
Decimal expansion of cube root of 6.
[ "1", "8", "1", "7", "1", "2", "0", "5", "9", "2", "8", "3", "2", "1", "3", "9", "6", "5", "8", "8", "9", "1", "2", "1", "1", "7", "5", "6", "3", "2", "7", "2", "6", "0", "5", "0", "2", "4", "2", "8", "2", "1", "0", "4", "6", "3", "1", "4", "1", "2", "1", "9", "6", "7", "1", "4", "8", "1", "3", "3", "4", "2", "9", "7", "9", "3", "1", "3", "0", "9", "7", "3", "9", "4", "5", "9", "3", "0", "1", "8", "6", "5", "6", "4", "7", "1", "4" ]
[ "nonn", "cons" ]
49
1
2
[ "A002949", "A005486", "A137914", "A319034" ]
[ "M4466" ]
N. J. A. Sloane
2023-08-21T11:25:41
oeisdata/seq/A005/A005486.seq
566595b286a38bce656cc9f8797f48d8
A005487
Starts 0, 4 and contains no 3-term arithmetic progression.
[ "0", "4", "5", "7", "11", "12", "16", "23", "26", "31", "33", "37", "38", "44", "49", "56", "73", "78", "80", "85", "95", "99", "106", "124", "128", "131", "136", "143", "169", "188", "197", "203", "220", "221", "226", "227", "238", "247", "259", "269", "276", "284", "287", "302", "308", "310", "313", "319", "337", "385", "392", "397", "422", "434", "455", "466", "470" ]
[ "nonn", "nice" ]
40
0
2
[ "A005487", "A033158", "A185256" ]
[ "M3243" ]
N. J. A. Sloane
2023-09-07T04:10:28
oeisdata/seq/A005/A005487.seq
27c7cf49a34d04a29bc9429322632301
A005488
Maximal number of edges in a b^{hat} graceful graph with n nodes.
[ "0", "1", "3", "6", "9", "13", "18", "24", "29" ]
[ "nonn", "more" ]
24
1
3
[ "A004137", "A005488", "A007187", "A239308" ]
[ "M2528" ]
N. J. A. Sloane, Simon Plouffe
2022-05-05T08:08:41
oeisdata/seq/A005/A005488.seq
dd3fdd23e3429cbe80911c46980feab1
A005489
Number of nonzero coefficients of order n in Baker-Campbell-Hausdorff expansion.
[ "1", "1", "2", "1", "8", "7", "32", "31", "96", "97", "512", "511", "2048", "2047", "7396", "7531", "32768", "32767", "131072", "131071", "508436", "512245", "2097152", "2097151", "8202208", "8207797", "33256980", "33335611", "134217728", "134217727", "536870912", "536870911", "2142108916", "2143603741", "8589928768", "8589921949" ]
[ "nonn", "nice" ]
21
1
3
null
[ "M0181" ]
David J. Thompson
2021-02-26T15:26:30
oeisdata/seq/A005/A005489.seq
2e172882fbc31be8a1a821bc9a50d8ff
A005490
Number of partitions of [n] where the first k elements are marked (0 <= k <= n-1) and at least k blocks contain their own index.
[ "1", "4", "13", "44", "163", "666", "2985", "14550", "76497", "430746", "2582447", "16403028", "109918745", "774289168", "5715471605", "44087879136", "354521950931", "2965359744446", "25749723493073", "231719153184018", "2157494726318233", "20753996174222510", "205985762120971167", "2106795754056142536" ]
[ "nonn" ]
35
1
2
[ "A000035", "A000110", "A005490", "A108087", "A259691", "A347420" ]
[ "M3467" ]
N. J. A. Sloane, Simon Plouffe
2022-04-24T06:31:43
oeisdata/seq/A005/A005490.seq
1a77ca5cfea4b10c4b2cc6241e934c43
A005491
a(n) = n^3 + 3*n + 1.
[ "1", "5", "15", "37", "77", "141", "235", "365", "537", "757", "1031", "1365", "1765", "2237", "2787", "3421", "4145", "4965", "5887", "6917", "8061", "9325", "10715", "12237", "13897", "15701", "17655", "19765", "22037", "24477", "27091", "29885", "32865", "36037", "39407", "42981", "46765", "50765", "54987", "59437", "64121", "69045" ]
[ "nonn", "easy" ]
39
0
2
[ "A000578", "A001093", "A005491", "A008585", "A016777", "A061989" ]
[ "M3855" ]
N. J. A. Sloane, Simon Plouffe
2022-12-01T17:46:08
oeisdata/seq/A005/A005491.seq
65b3e2f26f53ecd8833ff2d3dbc95dff
A005492
From expansion of falling factorials.
[ "4", "15", "52", "151", "372", "799", "1540", "2727", "4516", "7087", "10644", "15415", "21652", "29631", "39652", "52039", "67140", "85327", "106996", "132567", "162484", "197215", "237252", "283111", "335332", "394479", "461140", "535927", "619476", "712447", "815524", "929415", "1054852", "1192591", "1343412", "1508119", "1687540" ]
[ "nonn", "easy" ]
41
4
1
[ "A005490", "A005492", "A108087" ]
[ "M3495" ]
N. J. A. Sloane, Simon Plouffe
2022-12-02T07:05:38
oeisdata/seq/A005/A005492.seq
60c211337dccd8e8774dc90b30c0fb24
A005493
2-Bell numbers: a(n) = number of partitions of [n+1] with a distinguished block.
[ "1", "3", "10", "37", "151", "674", "3263", "17007", "94828", "562595", "3535027", "23430840", "163254885", "1192059223", "9097183602", "72384727657", "599211936355", "5150665398898", "45891416030315", "423145657921379", "4031845922290572", "39645290116637023", "401806863439720943", "4192631462935194064" ]
[ "nonn", "easy", "nice" ]
267
0
2
[ "A000110", "A005493", "A005494", "A008277", "A011968", "A011971", "A049020", "A106436", "A108087", "A124323", "A137650", "A143494", "A152433", "A159573", "A362924" ]
[ "M2851" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:28
oeisdata/seq/A005/A005493.seq
06e33ae5fdaf23b19ffb88cde6a20fab
A005494
3-Bell numbers: E.g.f.: exp(3*z + exp(z) - 1).
[ "1", "4", "17", "77", "372", "1915", "10481", "60814", "372939", "2409837", "16360786", "116393205", "865549453", "6713065156", "54190360453", "454442481041", "3952241526188", "35590085232519", "331362825860749", "3185554606447814", "31581598272055879", "322516283206446897" ]
[ "nonn" ]
89
0
2
[ "A000110", "A005493", "A005494", "A045379", "A108087", "A124323", "A196834" ]
[ "M3540" ]
N. J. A. Sloane, Simon Plouffe
2023-02-22T18:32:02
oeisdata/seq/A005/A005494.seq
21d9cb9ce29a10b906ccf3a39980b78c
A005495
Number of triangulations of the disk G_{n,3}.
[ "4", "16", "88", "538", "3568", "24596", "176354", "1298732", "9788838", "75190990", "586994548", "4646450800", "37225608048", "301400446752", "2463161448024", "20297411421166", "168503717726980", "1408243135178256", "11840473621942108", "100102553809842544" ]
[ "nonn" ]
25
0
1
null
[ "M3529" ]
N. J. A. Sloane
2023-04-25T13:12:51
oeisdata/seq/A005/A005495.seq
fcbcd518d51ce771138eef372b4e6924
A005496
A finite sequence associated with the Lie algebra E_7.
[ "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "20", "21", "24", "28", "29", "30", "31", "35", "36", "38", "39", "56", "60", "61", "62", "63", "84", "110", "111", "156", "159", "231", "399" ]
[ "nonn", "fini", "full" ]
5
0
2
null
null
N. J. A. Sloane.
2012-03-30T16:44:46
oeisdata/seq/A005/A005496.seq
69c4d31f0f5887a0d9894810dbc9dfb3
A005497
Erroneous version of A210696.
[ "1", "2", "5", "16", "48", "164", "599", "1952" ]
[ "dead" ]
19
0
2
null
[ "M1488" ]
N. J. A. Sloane.
2015-10-20T22:44:30
oeisdata/seq/A005/A005497.seq
1ba86943e05949ccaa352ff574a8cbe8
A005498
Triangulations of the disk G_{2,n}.
[ "1", "6", "21", "88", "330", "1302", "5005", "19504", "75582", "294140", "1144066", "4458192", "17383860", "67866918", "265182525", "1037169760", "4059928950", "15905412468", "62359143990", "244662838160", "960566918220", "3773656396796", "14833897694226", "58343359313568", "229591913401900", "903936171565752", "3560597348629860" ]
[ "nonn" ]
41
0
2
[ "A005498", "A262586" ]
[ "M4146" ]
N. J. A. Sloane
2024-11-23T14:27:45
oeisdata/seq/A005/A005498.seq
7c476413a8d7946dca06a708cb789bcb
A005499
Triangulations of the disk G_{3,n}.
[ "5", "26", "119", "538", "2310", "9882", "41715", "175088", "730626", "3037510", "12584726", "52003792", "214401024", "882233898", "3624161175", "14865947668", "60898934250", "249184153548", "1018532686314", "4159265561360", "16970015555220", "69183689403686", "281844056190294", "1147419353238816", "4668368905854840", "18982659409726792" ]
[ "nonn" ]
30
0
1
[ "A005499", "A262586" ]
[ "M3942" ]
N. J. A. Sloane
2024-11-23T14:27:41
oeisdata/seq/A005/A005499.seq
98b0320a05ea28ecbb279212ae38545c
A005500
Number of unrooted triangulations of a quadrilateral with n internal nodes.
[ "1", "2", "5", "18", "88", "489", "3071", "20667", "146381", "1072760", "8071728", "61990477", "484182622", "3835654678", "30757242535", "249255692801", "2038827903834", "16815060576958", "139706974995635", "1168468902294726", "9831504782276593", "83174244225508659", "707159273362126228", "6039827641569969225" ]
[ "nonn" ]
40
0
2
[ "A002710", "A005500", "A005505", "A169808" ]
[ "M1516" ]
N. J. A. Sloane
2021-02-23T10:05:55
oeisdata/seq/A005/A005500.seq
1217c50b742fd64553b9a8d02be84e34