Datasets:
christopher
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oeis

Dataset card Data Studio Files
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Community
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1999-12-11 03:00:00
2025-04-28 00:58:08
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A006401
Number of unsensed simple planar maps with n edges and without vertices of degree 1.
[ "1", "0", "0", "1", "1", "2", "5", "10", "28", "86", "285", "1055", "4211" ]
[ "nonn", "more" ]
22
0
6
[ "A006385", "A006389", "A006395", "A006400", "A006401", "A379436" ]
[ "M1384" ]
N. J. A. Sloane
2025-01-16T16:20:29
oeisdata/seq/A006/A006401.seq
fde38273f0a837876dbd90bba6ee6d96
A006402
Number of sensed 2-connected (nonseparable) planar maps with n edges.
[ "1", "2", "3", "6", "16", "42", "151", "596", "2605", "12098", "59166", "297684", "1538590", "8109078", "43476751", "236474942", "1302680941", "7256842362", "40832979283", "231838418310", "1327095781740", "7653155567834", "44434752082990", "259600430870176", "1525366978752096", "9010312253993072", "53485145730576790" ]
[ "nonn" ]
31
2
2
[ "A000087", "A000139", "A005645", "A006402", "A006403", "A006406", "A342061" ]
[ "M0812" ]
N. J. A. Sloane
2024-01-05T23:32:32
oeisdata/seq/A006/A006402.seq
13c55333934cb298187e4c13b60ec14a
A006403
Number of unsensed 2-connected planar maps with n edges.
[ "0", "1", "2", "3", "6", "15", "36", "114", "396", "1565", "6756", "31563", "154370", "785113", "4099948", "21870704", "118624544", "652485364", "3631820462", "20426666644", "115949791342", "663640383400", "3826858500878", "22218232389849", "129802836253994" ]
[ "nonn" ]
20
1
3
[ "A000139", "A006385", "A006402", "A006403", "A006407", "A006444", "A379432" ]
[ "M0808" ]
N. J. A. Sloane
2025-01-16T16:24:03
oeisdata/seq/A006/A006403.seq
abbad9fae2d08a98864d50e300d7abd2
A006404
Number of sensed 2-connected maps with n edges and without faces of degree 2.
[ "1", "1", "2", "5", "10", "29", "96", "339", "1320", "5473" ]
[ "nonn", "more" ]
18
3
3
[ "A006384", "A006402", "A006404", "A006405" ]
[ "M1385" ]
N. J. A. Sloane
2025-01-16T16:20:46
oeisdata/seq/A006/A006404.seq
d6f1a869e145964c911d83e0ea82109e
A006405
Number of unsensed 2-connected maps with n edges and without faces of degree 2.
[ "1", "1", "2", "5", "9", "24", "70", "222", "785", "3055" ]
[ "nonn", "more" ]
18
3
3
[ "A006385", "A006403", "A006405" ]
[ "M1365" ]
N. J. A. Sloane
2025-01-16T16:26:55
oeisdata/seq/A006/A006405.seq
775a2101a6ec441e894f1146cc829845
A006406
Number of sensed 2-connected simple planar maps with n edges.
[ "1", "1", "2", "4", "9", "24", "81", "274", "1071", "4357", "18416", "80040", "356109", "1610910", "7399114" ]
[ "nonn", "more" ]
30
3
3
[ "A006402", "A006404", "A006406", "A006407", "A342059", "A379437" ]
[ "M1195" ]
N. J. A. Sloane
2025-01-17T02:34:05
oeisdata/seq/A006/A006406.seq
349e1b270b8a7acbe1fb10114557cbd6
A006407
Number of unsensed 2-connected simple planar maps with n edges.
[ "1", "1", "2", "4", "8", "20", "58", "177", "630", "2410", "9772", "41423", "181586", "814412", "3722445" ]
[ "nonn", "more" ]
26
3
3
[ "A006403", "A006405", "A006406", "A006407", "A342060", "A379437" ]
[ "M1157" ]
N. J. A. Sloane
2025-01-17T02:32:49
oeisdata/seq/A006/A006407.seq
f6451cd1253ca26d535b20eaf7933b32
A006408
Number of nonseparable rooted toroidal maps with n + 3 edges and n + 1 vertices.
[ "4", "39", "190", "651", "1792", "4242", "8988", "17490", "31812", "54769", "90090", "142597", "218400", "325108", "472056", "670548", "934116", "1278795", "1723414", "2289903", "3003616", "3893670", "4993300", "6340230", "7977060", "9951669", "12317634", "15134665", "18469056", "22394152", "26990832", "32348008", "38563140" ]
[ "nonn" ]
21
2
1
[ "A006408", "A342989" ]
[ "M3672" ]
N. J. A. Sloane
2021-04-05T21:36:31
oeisdata/seq/A006/A006408.seq
78d38caa742ef330470639e1a2636a4e
A006409
Number of nonseparable rooted toroidal maps with n + 4 edges and n + 1 vertices.
[ "10", "190", "1568", "8344", "33580", "111100", "317680", "811096", "1891318", "4094090", "8328320", "16071120", "29636984", "52540472", "89974880", "149432720", "241497410", "380839382", "587453856", "888181800", "1318560100", "1925051700", "2767711440", "3923348520", "5489251950", "7587551010", "10370288640" ]
[ "nonn" ]
18
2
1
[ "A006409", "A342989" ]
[ "M4742" ]
N. J. A. Sloane
2021-04-05T21:36:45
oeisdata/seq/A006/A006409.seq
af18cc7ce6494b180af967a7d2db173b
A006410
Number of nonseparable rooted toroidal maps with n + 5 edges and n + 1 vertices.
[ "20", "651", "8344", "64667", "361884", "1607125", "5997992", "19535997", "57014776", "151986562", "375470160", "869285378", "1902886024", "3966657702", "7920130544", "15220758070", "28268206764", "50910912965", "89176474920", "152305796565", "254193384900", "415363487955", "665644575960", "1047743815755" ]
[ "nonn" ]
17
2
1
[ "A006410", "A342989" ]
[ "M5102" ]
N. J. A. Sloane
2021-04-05T18:50:28
oeisdata/seq/A006/A006410.seq
d7791e6468699a44e1f1c6c6da099653
A006411
Number of nonseparable tree-rooted planar maps with n + 2 edges and 3 vertices.
[ "3", "20", "75", "210", "490", "1008", "1890", "3300", "5445", "8580", "13013", "19110", "27300", "38080", "52020", "69768", "92055", "119700", "153615", "194810", "244398", "303600", "373750", "456300", "552825", "665028", "794745", "943950", "1114760", "1309440", "1530408", "1780240", "2061675", "2377620", "2731155", "3125538" ]
[ "nonn", "easy", "nice" ]
62
1
1
[ "A006411", "A006412", "A006413", "A027777", "A342984" ]
[ "M3073" ]
N. J. A. Sloane
2024-08-02T22:39:38
oeisdata/seq/A006/A006411.seq
adde526de8dcdf306178d510ca593947
A006412
Number of nonseparable tree-rooted planar maps with n + 3 edges and 4 vertices.
[ "4", "75", "604", "3150", "12480", "40788", "115500", "292578", "677820", "1459315", "2954952", "5679700", "10438272", "18449760", "31511880", "52213596", "84206100", "132543411", "204105220", "308116050", "456776320", "666022500", "956435220", "1354315950", "1892954700", "2614113099", "3569749200", "4824012424" ]
[ "nonn" ]
22
1
1
[ "A006411", "A006412", "A006413", "A342984" ]
[ "M3697" ]
N. J. A. Sloane
2021-04-05T21:37:06
oeisdata/seq/A006/A006412.seq
4dc94fa89a85b025a6dd4118f1149113
A006413
Number of nonseparable tree-rooted planar maps with n + 4 edges and 5 vertices.
[ "5", "210", "3150", "27556", "170793", "829920", "3359356", "11786190", "36845718", "104719524", "274707420", "672982128", "1554007910", "3407724936", "7139933088", "14366348780", "27878652291", "52364814150", "95497666810", "169546939380", "293722986375", "497527759560", "825473130300", "1343631834090" ]
[ "nonn" ]
20
1
1
[ "A006411", "A006412", "A006413", "A342984" ]
[ "M4031" ]
N. J. A. Sloane
2021-04-05T21:37:20
oeisdata/seq/A006/A006413.seq
998c6d6c95961a388005a4a11912f88f
A006414
Number of nonseparable toroidal tree-rooted maps with n + 2 edges and n + 1 vertices.
[ "1", "9", "40", "125", "315", "686", "1344", "2430", "4125", "6655", "10296", "15379", "22295", "31500", "43520", "58956", "78489", "102885", "133000", "169785", "214291", "267674", "331200", "406250", "494325", "597051", "716184", "853615", "1011375", "1191640", "1396736", "1629144", "1891505", "2186625", "2517480", "2887221" ]
[ "nonn", "easy" ]
92
0
2
[ "A004068", "A005891", "A006322", "A006414", "A006415", "A006434", "A006441", "A006542", "A133754", "A143945" ]
[ "M4621" ]
N. J. A. Sloane
2024-06-30T03:25:48
oeisdata/seq/A006/A006414.seq
8eb6fce9464afc2fd0ddea56af153bd6
A006415
Number of nonseparable toroidal tree-rooted maps with n + 3 edges and n + 1 vertices.
[ "4", "104", "1020", "6092", "26670", "94128", "283338", "754380", "1821534", "4061200" ]
[ "nonn", "more" ]
17
0
1
[ "A006414", "A006415", "A006441" ]
[ "M3705" ]
N. J. A. Sloane
2021-04-05T13:34:05
oeisdata/seq/A006/A006415.seq
8ae5a0bcd261aa71d582dced6f25f6bf
A006416
Number of loopless rooted planar maps with 3 faces and n vertices and no isthmuses. Also a(n)=T(4,n-3), array T as in A049600.
[ "1", "8", "20", "38", "63", "96", "138", "190", "253", "328", "416", "518", "635", "768", "918", "1086", "1273", "1480", "1708", "1958", "2231", "2528", "2850", "3198", "3573", "3976", "4408", "4870", "5363", "5888", "6446", "7038", "7665", "8328", "9028", "9766", "10543", "11360", "12218", "13118", "14061", "15048" ]
[ "nonn", "easy", "nice" ]
69
2
2
[ "A006416", "A049600", "A342980" ]
[ "M4490" ]
N. J. A. Sloane
2022-04-13T13:25:18
oeisdata/seq/A006/A006416.seq
9c558b0fbbbab79715cce6192923fb73
A006417
Number of loopless rooted planar maps with 4 faces and n vertices and no isthmuses.
[ "1", "20", "131", "469", "1262", "2862", "5780", "10725", "18647", "30784", "48713", "74405", "110284", "159290", "224946", "311429", "423645", "567308", "749023", "976373", "1258010", "1603750", "2024672", "2533221", "3143315", "3870456", "4731845", "5746501", "6935384", "8321522", "9930142", "11788805", "13927545", "16379012" ]
[ "nonn", "easy" ]
30
2
2
[ "A006417", "A342980" ]
[ "M5091" ]
N. J. A. Sloane
2024-07-18T08:51:31
oeisdata/seq/A006/A006417.seq
3e6af22a467cae41099646fc352ed749
A006418
Number of loopless rooted planar maps with 5 faces and n vertices and no isthmuses.
[ "1", "38", "469", "3008", "12843", "42602", "119042", "293578", "658021", "1367170", "2670203", "4953136", "8794967", "15040494", "24893192", "40031954", "62755945", "96162286", "144361777", "212738384", "308258755", "439838594", "618773310", "859240970", "1178886221", "1599494506", "2147766583", "2856204064" ]
[ "nonn" ]
22
2
2
[ "A006418", "A342980" ]
[ "M5268" ]
N. J. A. Sloane
2024-07-19T08:43:18
oeisdata/seq/A006/A006418.seq
57bd8f3a87a73e7a5ead20cbb43b32bf
A006419
a(n) = 2^(2*n+1) - C(2*n+3,n+1) + C(2*n+1,n).
[ "0", "1", "7", "37", "176", "794", "3473", "14893", "63004", "263950", "1097790", "4540386", "18696432", "76717268", "313889477", "1281220733", "5219170052", "21224674118", "86188320962", "349550141078", "1416102710912", "5731427140268", "23177285611082", "93655986978002", "378195990166136", "1526289367335244" ]
[ "nonn" ]
71
0
3
[ "A006419", "A342981" ]
[ "M4419" ]
N. J. A. Sloane
2021-04-06T20:24:50
oeisdata/seq/A006/A006419.seq
5485b743be13427fedbd738766e090e6
A006420
Number of rooted planar maps with 3 vertices and n faces and no isthmuses.
[ "1", "16", "150", "1104", "7077", "41504", "228810", "1205520", "6135690", "30391520", "147277676", "700990752", "3286733805", "15215673408", "69675615234", "316058238864", "1421891923038", "6350464644960", "28179908990772", "124327908683616", "545691921346146", "2383936774151616", "10370479696102500" ]
[ "nonn" ]
23
2
2
[ "A006420", "A342981" ]
[ "M5012" ]
N. J. A. Sloane
2024-12-29T03:40:52
oeisdata/seq/A006/A006420.seq
271b9d2c2e559b0942b4e9b6c001d9c6
A006421
Number of rooted planar maps with 4 vertices and n faces and no isthmuses.
[ "1", "30", "449", "4795", "41850", "319320", "2213665", "14283280", "87169790", "508887860", "2865204762", "15654301865", "83388235348", "434685964540", "2223970137825", "11194499812388", "55546566721430", "272142754971892", "1318317357277470", "6321681903231990", "30037740651227756", "141545610360126400" ]
[ "nonn" ]
21
2
2
[ "A006421", "A342981" ]
[ "M5211" ]
N. J. A. Sloane
2024-12-29T03:40:55
oeisdata/seq/A006/A006421.seq
da63e2c4a375c0da9d1045d7fa06a018
A006422
Number of rooted toroidal maps with 2 faces and n vertices and without separating cycles or isthmuses.
[ "4", "47", "240", "831", "2282", "5362", "11256", "21690", "39072", "66649", "108680", "170625", "259350", "383348", "552976", "780708", "1081404", "1472595", "1974784", "2611763", "3410946", "4403718", "5625800", "7117630", "8924760", "11098269", "13695192", "16778965", "20419886", "24695592", "29691552", "35501576" ]
[ "nonn" ]
17
1
1
[ "A006422", "A343090" ]
[ "M3684" ]
N. J. A. Sloane
2023-05-15T17:26:54
oeisdata/seq/A006/A006422.seq
f739bb8eeea3ac6ac0dd075407f76449
A006423
Number of rooted toroidal maps with 3 faces and n vertices and without separating cycles or isthmuses.
[ "10", "240", "2246", "12656", "52164", "173776", "495820", "1256992", "2902702", "6214208", "12494482", "23827440", "43430088", "76120288", "128926232", "211867328", "338940050", "529346384", "809006814", "1212404336", "1784810764", "2584951600", "3688170980", "5190163680", "7211346870", "9901950240", "13447909290" ]
[ "nonn" ]
12
1
1
[ "A006423", "A343090" ]
[ "M4748" ]
N. J. A. Sloane
2021-04-05T14:01:30
oeisdata/seq/A006/A006423.seq
a8163ecdacd69302f2faf166a5108bc2
A006424
Number of rooted toroidal maps with 4 faces and n vertices and without separating cycles or isthmuses.
[ "20", "831", "12656", "109075", "648792", "2978245", "11293436", "36973989", "107727724", "285451894", "699013380", "1601397330", "3465135024", "7135903782", "14072047976", "26707904230", "48991682628", "87164772761", "150869282184", "254695011933", "420306632200", "679327313795", "1077197343300", "1678276223715" ]
[ "nonn" ]
11
1
1
[ "A006424", "A343090" ]
[ "M5104" ]
N. J. A. Sloane
2021-04-05T14:00:38
oeisdata/seq/A006/A006424.seq
44a3f9a4de851ad66eda6f51861971e6
A006425
Number of rooted toroidal maps with 2 vertices and n faces and no isthmuses.
[ "4", "79", "900", "7885", "59080", "398846", "2499096", "14805705", "83969600", "459868530", "2447439384", "12718070274", "64766697520", "324156347260", "1598200903280", "7776728909121", "37404399901296", "178060831286890", "839857764202520", "3928581810398630", "18239060530882224", "84101317494787684" ]
[ "nonn" ]
10
1
1
[ "A006425", "A343092" ]
[ "M3700" ]
N. J. A. Sloane
2021-04-05T11:56:15
oeisdata/seq/A006/A006425.seq
ebf5ebdcca979d4f95bb4fb426eadeb3
A006426
Number of rooted toroidal maps with 3 vertices and n faces and no isthmuses.
[ "10", "340", "5846", "71372", "706068", "6052840", "46759630", "333746556", "2238411692", "14277544216", "87376309020", "516495616120", "2964332933800", "16586670357200", "90782049175614", "487329793111260", "2571575908919740", "13364166071956280", "68507393061864020", "346874109053120616" ]
[ "nonn" ]
10
1
1
[ "A006426", "A343092" ]
[ "M4751" ]
N. J. A. Sloane
2021-04-05T11:46:11
oeisdata/seq/A006/A006426.seq
f78da97e8baad0721da6b11b86d4a5f0
A006427
Number of rooted toroidal maps with 4 vertices and n faces and no isthmuses.
[ "20", "1071", "26320", "431739", "5494896", "58677420", "550712668", "4681144391", "36786186216", "271221867098", "1896796135920", "12688048319278", "81709791432384", "509222462694582", "3083998029716868", "18213177504318335", "105186858991413976", "595499805083872458", "3311524095424508480" ]
[ "nonn" ]
10
1
1
[ "A006427", "A343092" ]
[ "M5105" ]
N. J. A. Sloane
2021-04-05T11:45:31
oeisdata/seq/A006/A006427.seq
9ba024d6dbaf7111fccc0993279e8f42
A006428
Number of loopless tree-rooted planar maps with 3 vertices and n faces and no isthmuses.
[ "0", "3", "36", "135", "360", "798", "1568", "2826", "4770", "7645", "11748", "17433", "25116", "35280", "48480", "65348", "86598", "113031", "145540", "185115", "232848", "289938", "357696", "437550", "531050", "639873", "765828", "910861", "1077060", "1266660", "1482048", "1725768", "2000526", "2309195", "2654820", "3040623" ]
[ "nonn", "easy" ]
24
1
2
[ "A006428", "A342985" ]
[ "M3139" ]
N. J. A. Sloane
2022-08-08T21:55:58
oeisdata/seq/A006/A006428.seq
81f956f118a19abb54e8e62b1a32f8d9
A006429
Number of loopless tree-rooted planar maps with 4 vertices and n faces.
[ "0", "4", "135", "1368", "7350", "28400", "89073", "241220", "585057", "1301420", "2699125", "5282172", "9842430", "17584416", "30289835", "50530680", "81940901", "129557940", "200246795", "303220720", "450674190", "658545360", "947426925", "1343646044", "1880535825", "2599922780", "3553856649", "4806611060" ]
[ "nonn", "easy" ]
25
1
2
[ "A006429", "A342985" ]
[ "M3716" ]
N. J. A. Sloane
2025-01-25T02:16:48
oeisdata/seq/A006/A006429.seq
24987b7d3bcf43e48bf7abc48fcced66
A006430
Number of loopless tree-rooted planar maps with 5 vertices and n faces and no isthmuses.
[ "0", "5", "360", "7350", "73700", "474588", "2292790", "9046807", "30676440", "92393015", "252872984", "639382605", "1512137536", "3377126024", "7176513960", "14599539314", "28575632350", "54036739617", "99069119952", "176618150000", "306965183268", "521265871700", "866527603370", "1412513294049" ]
[ "nonn" ]
15
1
2
[ "A006430", "A342985" ]
[ "M4036" ]
N. J. A. Sloane
2021-04-04T13:39:28
oeisdata/seq/A006/A006430.seq
6c3a7a46651eed3369f96eb8b97ecfa1
A006431
Numbers that have a unique partition into a sum of four nonnegative squares.
[ "0", "1", "2", "3", "5", "6", "7", "8", "11", "14", "15", "23", "24", "32", "56", "96", "128", "224", "384", "512", "896", "1536", "2048", "3584", "6144", "8192", "14336", "24576", "32768", "57344", "98304", "131072", "229376", "393216", "524288", "917504", "1572864", "2097152", "3670016", "6291456", "8388608", "14680064" ]
[ "nonn", "easy", "nice" ]
71
1
3
[ "A002635", "A006431", "A180149", "A245022" ]
null
David M. Bloom
2024-10-19T15:57:32
oeisdata/seq/A006/A006431.seq
ea873856883c93fb3d5be2baf4482d55
A006432
Number of tree-rooted planar maps with 3 vertices and n faces and no isthmuses.
[ "0", "3", "60", "650", "5352", "37681", "239752", "1421226", "7996160", "43219990", "226309800", "1154900708", "5769562736", "28312118565", "136830224464", "652656300122", "3077631550512", "14367512295274", "66478236840680", "305161336656876", "1390869368495728", "6298727501142218", "28358908010334960" ]
[ "nonn" ]
12
1
2
[ "A006432", "A342987" ]
[ "M3166" ]
N. J. A. Sloane
2021-04-06T21:12:43
oeisdata/seq/A006/A006432.seq
d03f9d88d63fdaffc7a545705967208d
A006433
Number of tree-rooted planar maps with 4 vertices and n faces and no isthmuses.
[ "0", "4", "175", "3324", "42469", "429120", "3711027", "28723640", "204598130", "1366223880", "8664086470", "52673351080", "309164754285", "1761471681568", "9783594370723", "53154274959360", "283267669144390", "1484104565936920", "7658877239935362", "38993558097982312", "196127054929939810" ]
[ "nonn" ]
17
1
2
[ "A006433", "A342987" ]
[ "M3720" ]
N. J. A. Sloane
2021-04-06T21:13:05
oeisdata/seq/A006/A006433.seq
cc5b7716a3b5d1f0a3041c443843204a
A006434
Number of tree-rooted toroidal maps with 2 faces and n vertices and without separating loops or isthmuses.
[ "4", "120", "1230", "7424", "32424", "113584", "338742", "893220", "2136618", "4721728", "9770904" ]
[ "nonn", "more" ]
13
1
1
[ "A006434", "A006435", "A006436", "A006439" ]
[ "M3708" ]
N. J. A. Sloane
2021-04-04T13:42:33
oeisdata/seq/A006/A006434.seq
8566b607360b4bed770cda23845453a5
A006435
Number of tree-rooted toroidal maps with 3 faces and n vertices and without separating loops or isthmuses.
[ "10", "705", "14478", "154420", "1092640", "5826492", "25240410", "93203561", "303143970", "889015725" ]
[ "nonn", "more" ]
10
1
1
[ "A006434", "A006435" ]
[ "M4755" ]
N. J. A. Sloane
2021-04-04T13:43:29
oeisdata/seq/A006/A006435.seq
0340c1669edd80919327ca7e267586c9
A006436
Number of tree-rooted toroidal maps with 2 faces and n vertices and without isthmuses.
[ "10", "192", "1630", "8924", "36834", "124560", "362934", "941820", "2227368", "4881448", "889015725" ]
[ "nonn", "more" ]
9
1
1
[ "A006436", "A006437" ]
[ "M4743" ]
N. J. A. Sloane
2021-04-04T13:43:52
oeisdata/seq/A006/A006436.seq
bfddfb4582e0d2e9eaf96405cfa749f3
A006437
Number of tree-rooted toroidal maps with 3 faces and n vertices and without isthmuses.
[ "70", "2330", "32130", "271285", "1655800", "7997850", "32332170", "113568455", "355905030" ]
[ "nonn", "more" ]
10
1
1
[ "A006436", "A006437" ]
[ "M5342" ]
N. J. A. Sloane
2021-04-04T13:40:39
oeisdata/seq/A006/A006437.seq
1641bbecb807c26f6a8942e1fe7ede2f
A006438
Expansion of e.g.f. 1/sqrt(1-8x+x^2).
[ "1", "4", "47", "924", "25449", "901380", "39024495", "1996824060", "117897243345", "7889215807620", "590030724668175", "48773659291364700", "4415782937120703225", "434554886774113805700", "46185660455230892170575", "5272363854999057185869500", "643381344417456140309438625" ]
[ "nonn" ]
13
0
2
null
null
N. J. A. Sloane.
2020-01-30T21:29:14
oeisdata/seq/A006/A006438.seq
7271410a6e6c7d92a12f1cc91fbd6d7c
A006439
Number of tree-rooted toroidal maps with 2 faces and n vertices and without separating loops.
[ "4", "152", "2630", "31500", "303534", "2530976", "19030428", "132386340", "866782510", "5405853200" ]
[ "nonn", "more" ]
11
1
1
[ "A006439", "A006440" ]
[ "M3719" ]
N. J. A. Sloane
2021-04-04T13:44:44
oeisdata/seq/A006/A006439.seq
0859105ad92f3484b656b6f951fef298
A006440
Number of tree-rooted toroidal maps with 3 faces and n vertices and without separating loops.
[ "10", "805", "23730", "431319", "5862920", "65548890", "636520890", "5555779185", "44603489700" ]
[ "nonn", "more" ]
9
1
1
[ "A006439", "A006440" ]
[ "M4756" ]
N. J. A. Sloane
2021-04-04T13:45:01
oeisdata/seq/A006/A006440.seq
c6c009df98c5120ba5fba81c2d634c2b
A006441
Number of nonseparable toroidal tree-rooted maps with n + 4 edges and n + 1 vertices.
[ "10", "595", "11010", "111650", "773640", "4104225", "17838730", "66390610", "218140650" ]
[ "nonn", "more" ]
9
0
1
[ "A006414", "A006415", "A006441" ]
[ "M4754" ]
N. J. A. Sloane
2021-04-05T11:58:21
oeisdata/seq/A006/A006441.seq
93315c5121b837a653252589a4ad3ed9
A006442
Expansion of 1/sqrt(1 - 10*x + x^2).
[ "1", "5", "37", "305", "2641", "23525", "213445", "1961825", "18205345", "170195525", "1600472677", "15122515985", "143457011569", "1365435096485", "13033485491077", "124715953657025", "1195966908404545", "11490534389896325", "110584004488276645", "1065853221648055025" ]
[ "nonn", "easy" ]
94
0
2
[ "A000012", "A001850", "A006442", "A084768", "A084769", "A098270", "A243943" ]
null
N. J. A. Sloane
2023-05-21T21:52:35
oeisdata/seq/A006/A006442.seq
cf078a8825cf4340776c8b4af1bef90c
A006443
Number of achiral planar maps with n edges.
[ "1", "2", "4", "14", "47", "184", "761", "3314", "14997", "69886", "333884", "1626998", "8067786", "40580084", "206734083", "1064666724", "5536480877", "29036188788", "153450351924", "816503772830", "4371551433888" ]
[ "nonn", "nice", "more" ]
34
0
2
[ "A006384", "A006385", "A006443", "A006444", "A006445", "A380234" ]
[ "M1277" ]
N. J. A. Sloane
2025-01-20T20:24:47
oeisdata/seq/A006/A006443.seq
bfcfeab9e439721e1f54fed5a633f78c
A006444
Number of achiral 2-connected planar maps with n edges.
[ "0", "1", "2", "3", "6", "14", "30", "77", "196", "525", "1414", "3960", "11056", "31636", "90818", "264657", "774146", "2289787", "6798562", "20354005", "61164374", "184985060", "561433922", "1712696708", "5241637812" ]
[ "nonn" ]
16
1
3
[ "A006402", "A006403", "A006443", "A006444", "A006445" ]
[ "M0804" ]
N. J. A. Sloane
2025-01-14T19:13:11
oeisdata/seq/A006/A006444.seq
dfb9fcef1ec530605ad02af9b7d27ffc
A006445
Number of n-edge 3-connected planar maps with a sense-reversing automorphism.
[ "0", "0", "0", "0", "0", "1", "0", "1", "2", "1", "4", "9", "12", "27", "50", "99", "188", "386", "740", "1528", "3012", "6192", "12376", "25594", "51628", "107135", "218100", "453895", "930812", "1943281", "4009512", "8394915", "17414512" ]
[ "nonn" ]
13
1
9
null
[ "M0172" ]
N. J. A. Sloane, T. R. S. Walsh, personal communication
2018-01-10T17:19:01
oeisdata/seq/A006/A006445.seq
a6d478d6f3ad04287f4de2050dd388f8
A006446
Numbers k such that floor(sqrt(k)) divides k.
[ "1", "2", "3", "4", "6", "8", "9", "12", "15", "16", "20", "24", "25", "30", "35", "36", "42", "48", "49", "56", "63", "64", "72", "80", "81", "90", "99", "100", "110", "120", "121", "132", "143", "144", "156", "168", "169", "182", "195", "196", "210", "224", "225", "240", "255", "256", "272", "288", "289", "306", "323", "324", "342", "360", "361", "380", "399", "400", "420" ]
[ "nonn", "easy", "nice" ]
83
1
2
[ "A000196", "A006446", "A035106", "A066377", "A087811" ]
[ "M0548" ]
N. J. A. Sloane
2022-09-24T05:48:21
oeisdata/seq/A006/A006446.seq
d68e7d9d4222a78c4178285e486db877
A006447
Consider a 2-D cellular automaton generated by the Schrandt-Ulam rule of A170896, but confined to a semi-infinite strip of width n, starting with one ON cell at the top left corner; a(n) is the period of the resulting structure.
[ "1", "2", "3", "5", "5", "8", "13", "13", "13", "26", "13", "91", "13", "106", "106", "75", "93", "62", "80", "132", "337", "416", "62", "62", "62", "271", "34", "155", "525", "548", "1084", "115", "62", "558", "62", "1500", "2922", "124", "2958", "3374", "2323", "4183", "8073", "7925", "744", "2298", "434", "6700", "310", "23796", "12732", "26405" ]
[ "nonn" ]
27
1
2
null
[ "M0608" ]
N. J. A. Sloane
2017-10-04T00:53:26
oeisdata/seq/A006/A006447.seq
373c75a7ae8d6a0b8767ae87afa5eebf
A006448
Number of n-element algebras with 1 binary operator and 1 constant (pointed groupoids).
[ "1", "16", "9882", "715860992", "12417636281312500", "85953540009068492207916672", "356838302112667713247240882121025536249", "1245456693529103515171728481423145699858332531028201472" ]
[ "nonn", "easy", "nice" ]
29
1
2
[ "A001329", "A006448" ]
[ "M5029" ]
N. J. A. Sloane
2021-12-19T12:01:42
oeisdata/seq/A006/A006448.seq
7b6b1a80699de5a5be2bf5b00a1baa70
A006449
Row sums of Fibonacci-Pascal triangle in A045995.
[ "1", "2", "3", "6", "16", "122", "8003", "18476850", "190844194212235", "192303711247038132600144086", "20672849468072409216994337223266361373129558839387316" ]
[ "nonn", "nice" ]
25
0
2
[ "A006449", "A045995" ]
[ "M0813" ]
Jeffrey Shallit, Nov 25 1975
2025-01-05T19:51:33
oeisdata/seq/A006/A006449.seq
5b6ed09e2ab481ed90b56f049d7e737d
A006450
Prime-indexed primes: primes with prime subscripts.
[ "3", "5", "11", "17", "31", "41", "59", "67", "83", "109", "127", "157", "179", "191", "211", "241", "277", "283", "331", "353", "367", "401", "431", "461", "509", "547", "563", "587", "599", "617", "709", "739", "773", "797", "859", "877", "919", "967", "991", "1031", "1063", "1087", "1153", "1171", "1201", "1217", "1297", "1409", "1433", "1447", "1471" ]
[ "easy", "nice", "nonn" ]
177
1
1
[ "A000040", "A006450", "A007821", "A018252", "A038580", "A049076", "A049078", "A049090", "A049202", "A049203", "A057847", "A057849", "A057850", "A057851", "A058332", "A078782", "A093047", "A102615", "A102616", "A102617", "A185723", "A185724", "A213356", "A214296", "A270792", "A270794", "A270795", "A270796" ]
[ "M2477" ]
Jeffrey Shallit, Nov 25 1975
2025-02-16T08:32:30
oeisdata/seq/A006/A006450.seq
dcd06ed4ff146e9ac664d8048cec78ba
A006451
Numbers k such that k*(k+1)/2 + 1 is a square.
[ "0", "2", "5", "15", "32", "90", "189", "527", "1104", "3074", "6437", "17919", "37520", "104442", "218685", "608735", "1274592", "3547970", "7428869", "20679087", "43298624", "120526554", "252362877", "702480239", "1470878640", "4094354882", "8572908965", "23863649055", "49966575152" ]
[ "nonn", "easy" ]
127
0
2
[ "A000124", "A000217", "A001652", "A001921", "A006451", "A006452", "A006454", "A098586", "A098790", "A129556", "A233450" ]
[ "M1472" ]
N. J. A. Sloane and Jeffrey Shallit
2022-04-13T13:25:18
oeisdata/seq/A006/A006451.seq
719bb7271789ad444799b3390ee98d0b
A006452
a(n) = 6*a(n-2) - a(n-4).
[ "1", "1", "2", "4", "11", "23", "64", "134", "373", "781", "2174", "4552", "12671", "26531", "73852", "154634", "430441", "901273", "2508794", "5253004", "14622323", "30616751", "85225144", "178447502", "496728541", "1040068261", "2895146102", "6061962064", "16874148071", "35331704123" ]
[ "nonn", "easy" ]
102
0
3
[ "A001333", "A006451", "A006452", "A006454", "A038723", "A077446", "A216134", "A217278" ]
[ "M1245" ]
N. J. A. Sloane, Jeffrey Shallit
2023-01-23T05:00:01
oeisdata/seq/A006/A006452.seq
9739d838580dfe5bca67cdaaa4eaba84
A006453
Expansion of 1/sqrt(1 - 12x + x^2).
[ "1", "6", "107", "3186", "132849", "7122870", "466788195", "36153055890", "3230902408545", "327238250094630", "37043457415695675", "4634751809368192050", "635113491345511326225", "94599619441277679278550" ]
[ "nonn" ]
13
0
2
null
null
N. J. A. Sloane
2021-12-26T21:33:09
oeisdata/seq/A006/A006453.seq
93c58882c99c26340eb77aad45d69df8
A006454
Solution to a Diophantine equation: each term is a triangular number and each term + 1 is a square.
[ "0", "3", "15", "120", "528", "4095", "17955", "139128", "609960", "4726275", "20720703", "160554240", "703893960", "5454117903", "23911673955", "185279454480", "812293020528", "6294047334435", "27594051024015", "213812329916328", "937385441796000", "7263325169820735", "31843510970040003", "246739243443988680" ]
[ "nonn", "easy" ]
120
0
2
[ "A000217", "A001109", "A006451", "A006452", "A006454", "A054504", "A081119", "A124174", "A182334", "A216134", "A216162", "A217278", "A245031", "A285955", "A285985" ]
[ "M3004" ]
N. J. A. Sloane, Jeffrey Shallit
2025-02-16T08:32:30
oeisdata/seq/A006/A006454.seq
0b37528d389157140c2712156d33b0a6
A006455
Number of partial orders on {1,2,...,n} that are contained in the usual linear order (i.e., xRy => x<y).
[ "1", "1", "2", "7", "40", "357", "4824", "96428", "2800472", "116473461", "6855780268", "565505147444", "64824245807684" ]
[ "hard", "more", "nice", "nonn" ]
68
0
3
[ "A000112", "A001035", "A006455", "A323502" ]
[ "M1805" ]
N. J. A. Sloane
2024-04-24T13:24:57
oeisdata/seq/A006/A006455.seq
7dbb9a9b597e2c18f28134524fe9c1a0
A006456
Number of compositions (ordered partitions) of n into squares.
[ "1", "1", "1", "1", "2", "3", "4", "5", "7", "11", "16", "22", "30", "43", "62", "88", "124", "175", "249", "354", "502", "710", "1006", "1427", "2024", "2870", "4068", "5767", "8176", "11593", "16436", "23301", "33033", "46832", "66398", "94137", "133462", "189211", "268252", "380315", "539192", "764433", "1083764", "1536498", "2178364" ]
[ "nonn", "easy" ]
70
0
5
[ "A006456", "A280542", "A337165" ]
[ "M0528" ]
N. J. A. Sloane
2021-02-04T15:21:57
oeisdata/seq/A006/A006456.seq
bf30aa7d14f6b3daa8e7809b4169cff2
A006457
Number of elements in Z[ i ] whose 'smallest algorithm' is <= n.
[ "1", "5", "17", "49", "125", "297", "669", "1457", "3093", "6457", "13309", "27201", "55237", "111689", "225101", "452689", "908885", "1822809", "3652701", "7315553", "14645349", "29311081", "58650733", "117342321", "234741877", "469565561", "939245693", "1878655105", "3757539461", "7515406473", "15031271565" ]
[ "nonn", "easy", "nice" ]
49
0
2
[ "A006457", "A006458", "A006459" ]
[ "M3873" ]
H. W. Lenstra, Jr.
2022-05-30T02:26:49
oeisdata/seq/A006/A006457.seq
d5fff1318e96eb866f17614d595f8944
A006458
Number of elements in Z[ omega ] whose 'smallest algorithm' is <= n, where omega^2 = -omega - 1.
[ "1", "7", "31", "115", "391", "1267", "3979", "12271", "37423", "113371", "342091", "1029799", "3095671", "9298147", "27914179", "83777503", "251394415", "754292827", "2263072411", "6789560407", "20369288455", "61108939795", "183328720435", "549989524879", "1649974525855", "4949934107083", "14849820951115" ]
[ "nonn", "easy", "nice" ]
44
0
2
[ "A006457", "A006458", "A006459" ]
[ "M4399" ]
H. W. Lenstra, Jr.
2022-01-28T07:44:29
oeisdata/seq/A006/A006458.seq
cb72a66ba467a930ba40669e4c41972c
A006459
Number of elements in Z[ sqrt(-2) ] whose 'smallest algorithm' is <= n.
[ "1", "3", "9", "17", "31", "53", "85", "133", "197", "293", "417", "593", "849", "1193", "1661", "2291", "3139", "4299" ]
[ "nonn", "more" ]
19
0
2
[ "A006457", "A006458", "A006459" ]
[ "M2771" ]
H. W. Lenstra, Jr.
2022-01-27T23:41:36
oeisdata/seq/A006/A006459.seq
2ebf206691628bebed94165cdfa41e9c
A006460
Image of n after 3k iterates of '3x+1' map (k large).
[ "1", "2", "2", "4", "4", "4", "2", "1", "2", "1", "4", "1", "1", "4", "4", "2", "1", "4", "4", "2", "2", "1", "1", "2", "4", "2", "1", "1", "1", "1", "2", "4", "4", "2", "2", "1", "1", "1", "2", "4", "2", "4", "4", "2", "2", "2", "4", "4", "1", "1", "1", "4", "4", "2", "2", "2", "4", "2", "4", "2", "2", "4", "4", "1", "1", "1", "1", "4", "4", "4", "1", "2", "2", "2", "4", "2", "2", "4", "4", "1", "2", "4", "4", "1", "1", "1", "1", "4", "1", "4", "4", "4", "4", "1", "1", "1", "2", "2", "2", "2", "2", "2", "1", "1", "4" ]
[ "nonn", "nice" ]
32
1
2
[ "A006370", "A006460", "A076052", "A139399" ]
[ "M0304" ]
N. J. A. Sloane
2022-08-08T15:54:08
oeisdata/seq/A006/A006460.seq
d2ebc5ad0daa326452c898392da86cf8
A006461
Percolation series for directed square lattice.
[ "1", "0", "-1", "-2", "-4", "-8", "-17", "-38", "-88", "-210", "-511", "-1264", "-3165", "-8006", "-20426", "-52472", "-135682", "-352562", "-920924", "-2414272", "-6356565", "-16782444", "-44470757", "-118090648", "-314580062", "-839379548", "-2245969278", "-6017177104", "-16161597987" ]
[ "sign", "nice" ]
19
0
4
[ "A006461", "A006462" ]
[ "M1144" ]
N. J. A. Sloane, Simon Plouffe
2019-01-08T05:15:55
oeisdata/seq/A006/A006461.seq
d61d1c3667c419d072074f73430320da
A006462
Percolation series for directed square lattice.
[ "1", "0", "-1", "-2", "-2", "0", "2", "4", "3", "0", "-1", "6", "28", "72", "139", "242", "407", "722", "1215", "2348", "3753", "7186", "9558", "21800", "16576", "61234", "-7978", "226136", "-446034", "1118180", "-3180033", "6428640", "-24607343", "56904504", "-176451720", "379824634", "-1133204742", "3043377452", "-9446665098", "25288847986" ]
[ "sign" ]
11
0
4
[ "A006461", "A006462" ]
[ "M0186" ]
N. J. A. Sloane
2024-11-28T11:04:13
oeisdata/seq/A006/A006462.seq
ead3973278d59dff659e6178dcad450d
A006463
Convolve natural numbers with characteristic function of triangular numbers.
[ "0", "0", "1", "2", "4", "6", "8", "11", "14", "17", "20", "24", "28", "32", "36", "40", "45", "50", "55", "60", "65", "70", "76", "82", "88", "94", "100", "106", "112", "119", "126", "133", "140", "147", "154", "161", "168", "176", "184", "192", "200", "208", "216", "224", "232", "240", "249", "258", "267", "276", "285", "294", "303", "312", "321", "330", "340", "350", "360" ]
[ "nonn", "easy", "nice", "changed" ]
65
0
4
[ "A003056", "A006463", "A010054", "A060432", "A074909", "A076269" ]
null
N. J. A. Sloane
2025-04-24T17:05:49
oeisdata/seq/A006/A006463.seq
9e581b990092043aa8a51d28b21e4df8
A006464
Continued fraction for Sum_{n>=0} 1/4^(2^n).
[ "0", "3", "6", "4", "4", "2", "4", "6", "4", "2", "6", "4", "2", "4", "4", "6", "4", "2", "6", "4", "4", "2", "4", "6", "2", "4", "6", "4", "2", "4", "4", "6", "4", "2", "6", "4", "4", "2", "4", "6", "4", "2", "6", "4", "2", "4", "4", "6", "2", "4", "6", "4", "4", "2", "4", "6", "2", "4", "6", "4", "2", "4", "4", "6", "4", "2", "6", "4", "4", "2", "4", "6", "4", "2", "6", "4", "2", "4", "4", "6", "4", "2", "6", "4", "4", "2", "4", "6", "2", "4", "6", "4", "2", "4", "4", "6", "2", "4", "6", "4", "4", "2", "4", "6", "4" ]
[ "nonn", "cofr" ]
29
0
2
null
[ "M2512" ]
N. J. A. Sloane
2017-08-30T17:49:38
oeisdata/seq/A006/A006464.seq
f7d585f89242f099e8d827c58cae79e8
A006465
Continued fraction for 4^5*Sum_{n>=0} 1/4^(2^n).
[ "324", "63", "1", "1023", "64", "1023", "1", "63", "1023", "1", "63", "1023", "1", "62", "1", "1023", "63", "1", "1023", "64", "1023", "1", "63", "1023", "1", "62", "1", "1023", "64", "1023", "1", "63", "1023", "1", "62", "1", "1023", "63", "1", "1023", "63", "1", "1023", "64", "1023", "1" ]
[ "nonn", "cofr" ]
23
0
1
[ "A006465", "A160387" ]
[ "M5437" ]
N. J. A. Sloane
2017-08-30T17:49:57
oeisdata/seq/A006/A006465.seq
e2304a8bd54517859d8acf5cba6c1ddb
A006466
Continued fraction expansion of C = 2*Sum_{n>=0} 1/2^(2^n).
[ "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2", "1", "1", "1", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "1", "1", "1", "2", "1", "2" ]
[ "nonn", "cofr" ]
34
0
5
[ "A006466", "A076214" ]
[ "M0049" ]
N. J. A. Sloane
2017-08-30T17:50:19
oeisdata/seq/A006/A006466.seq
76d18c38f255b0df735861bf99918880
A006467
Continued fraction for Sum_{n>=0} (-1)^n/3^(2^n).
[ "0", "4", "3", "1", "3", "5", "1", "3", "5", "3", "3", "1", "5", "3", "1", "3", "3", "5", "3", "1", "3", "5", "1", "3", "3", "5", "3", "1", "5", "3", "1", "3", "5", "3", "3", "1", "3", "5", "1", "3", "5", "3", "3", "1", "5", "3", "1", "3", "5", "3", "3", "1", "3", "5", "1", "3", "3", "5", "3", "1", "5", "3", "1", "3", "3", "5", "3", "1", "3", "5", "1", "3", "5", "3", "3", "1", "5", "3", "1", "3", "3", "5", "3", "1", "3", "5", "1", "3", "3", "5", "3", "1", "5", "3", "1", "3", "3", "5", "3", "1", "3", "5", "1", "3", "5" ]
[ "nonn", "cofr" ]
26
0
2
[ "A006467", "A160386" ]
[ "M3206" ]
N. J. A. Sloane
2017-08-30T17:50:32
oeisdata/seq/A006/A006467.seq
12adf6950e8cfd35d1a76e7a6f2bbfa7
A006468
Number of rooted planar maps with 4 faces and n vertices and no isthmuses.
[ "5", "37", "150", "449", "1113", "2422", "4788", "8790", "15213", "25091", "39754", "60879", "90545", "131292", "186184", "258876", "353685", "475665", "630686", "825517", "1067913", "1366706", "1731900", "2174770", "2707965", "3345615", "4103442", "4998875", "6051169", "7281528", "8713232", "10371768", "12284965", "14483133", "16999206" ]
[ "nonn" ]
30
1
1
[ "A006468", "A342981" ]
[ "M3984" ]
N. J. A. Sloane
2021-04-02T19:55:26
oeisdata/seq/A006/A006468.seq
8c454c7690c4705d00296cb7f00621d4
A006469
Number of rooted toroidal maps with 2 faces, n vertices and no isthmuses.
[ "10", "79", "340", "1071", "2772", "6258", "12768", "24090", "42702", "71929", "116116", "180817", "273000", "401268", "576096", "810084", "1118226", "1518195", "2030644", "2679523", "3492412", "4500870", "5740800", "7252830", "9082710", "11281725", "13907124", "17022565", "20698576", "25013032", "30051648", "35908488" ]
[ "nonn", "easy" ]
32
1
1
[ "A006469", "A343092" ]
[ "M4727" ]
N. J. A. Sloane
2021-04-05T11:57:55
oeisdata/seq/A006/A006469.seq
ec9dafee349c480b9ad94dfb2aaea2aa
A006470
Number of tree-rooted planar maps with 3 faces and n vertices and no isthmuses.
[ "2", "15", "60", "175", "420", "882", "1680", "2970", "4950", "7865", "12012", "17745", "25480", "35700", "48960", "65892", "87210", "113715", "146300", "185955", "233772", "290950", "358800", "438750", "532350", "641277", "767340", "912485", "1078800", "1268520", "1484032", "1727880", "2002770", "2311575", "2657340", "3043287", "3472820", "3949530", "4477200", "5059810", "5701542", "6406785", "7180140" ]
[ "nonn", "easy" ]
61
1
1
[ "A006470", "A027789", "A108838", "A342987" ]
[ "M2075" ]
N. J. A. Sloane
2024-07-18T11:35:50
oeisdata/seq/A006/A006470.seq
b3b97173155f240daea27dc8b565138c
A006471
Number of tree-rooted planar maps with 4 faces and n vertices and no isthmuses.
[ "5", "84", "650", "3324", "13020", "42240", "118998", "300300", "693693", "1490060", "3011580", "5779592", "10608000", "18728832", "31957620", "52907400", "85261341", "134115300", "206402966", "311417700", "461446700", "672534720", "965396250", "1366496820", "1909325925", "2635885980", "3598423704", "4861432400", "6503955744", "8622225920" ]
[ "nonn" ]
21
1
1
[ "A006471", "A342987" ]
[ "M4021" ]
N. J. A. Sloane
2021-04-04T13:19:17
oeisdata/seq/A006/A006471.seq
f050565301e7b4a50d31a25a64800b29
A006472
a(n) = n!*(n-1)!/2^(n-1).
[ "1", "1", "3", "18", "180", "2700", "56700", "1587600", "57153600", "2571912000", "141455160000", "9336040560000", "728211163680000", "66267215894880000", "6958057668962400000", "834966920275488000000", "113555501157466368000000", "17373991677092354304000000", "2970952576782792585984000000" ]
[ "nonn", "easy", "nice" ]
205
1
3
[ "A000110", "A000258", "A001044", "A002846", "A005121", "A006472", "A084939", "A084940", "A084941", "A084942", "A084943", "A084944", "A123385", "A213427", "A317145" ]
[ "M3052" ]
N. J. A. Sloane
2025-02-25T09:45:19
oeisdata/seq/A006/A006472.seq
0bdc2228f85c3d4f552d98fab316e595
A006473
a(n) = binomial(n,2)!/n!.
[ "1", "30", "30240", "1816214400", "10137091700736000", "7561714896123855667200000", "1025113885554181044609786839040000000", "32964677266721834921175915315161407370035200000000", "318071672921132854486459356650996997744817246158245068800000000000" ]
[ "nonn" ]
48
3
2
null
[ "M5217" ]
N. J. A. Sloane
2017-10-04T00:17:21
oeisdata/seq/A006/A006473.seq
d651310505f38ba7bf91a4cff367526d
A006474
Related to Ramsey numbers.
[ "1", "2", "4", "9", "16", "20", "30", "42", "49", "64" ]
[ "nonn" ]
7
1
2
null
[ "M1167" ]
N. J. A. Sloane.
2012-03-30T16:44:58
oeisdata/seq/A006/A006474.seq
98a7c8f93462b6c6c08c389b64f6df41
A006475
Number of 2-tournaments on n nodes.
[ "2", "324", "48869983488" ]
[ "nonn", "bref" ]
11
4
1
null
[ "M2185" ]
N. J. A. Sloane.
2012-03-30T16:44:58
oeisdata/seq/A006/A006475.seq
66f27908fd5b689fc4c1b02f95ccfc8f
A006476
From relations between Siegel theta series.
[ "389", "433", "563", "571", "643", "709", "997", "1061", "1171", "1483", "1531", "1567", "1613", "1621", "1627", "1693", "1873", "1907", "1913", "1933", "2027", "2029", "2081", "2089", "2251", "2293", "2333", "2381", "2593", "2609", "2617", "2677", "2797", "2837", "2843", "2861", "2953", "2963", "3019", "3089", "3271", "3463", "3583", "3701", "3779", "3911", "3943", "3967", "4027", "4093", "4139", "4217", "4253", "4357", "4481", "4547", "4787", "4799", "4951", "5003" ]
[ "nonn", "nice" ]
18
1
1
null
[ "M5449" ]
N. J. A. Sloane
2021-12-19T00:21:22
oeisdata/seq/A006/A006476.seq
7dca803731a2c8c1e3b8f340f9eefc6e
A006477
Number of partitions of n with at least 1 odd and 1 even part.
[ "0", "0", "0", "1", "1", "4", "4", "10", "11", "22", "25", "44", "51", "83", "98", "149", "177", "259", "309", "436", "521", "716", "857", "1151", "1376", "1816", "2170", "2818", "3361", "4309", "5132", "6502", "7728", "9695", "11501", "14298", "16924", "20877", "24661", "30203", "35598", "43323", "50956", "61651", "72357", "87086", "101999" ]
[ "nonn" ]
22
0
6
[ "A006477", "A038348", "A047967" ]
[ "M3232" ]
N. J. A. Sloane.
2014-03-17T10:41:12
oeisdata/seq/A006/A006477.seq
2e39b56c40ede8a1cc1fb1b9678b5b6e
A006478
a(n) = a(n-1) + a(n-2) + F(n) - 1, a(0) = a(1) = 0, where F() = Fibonacci numbers A000045.
[ "0", "0", "0", "1", "3", "8", "18", "38", "76", "147", "277", "512", "932", "1676", "2984", "5269", "9239", "16104", "27926", "48210", "82900", "142055", "242665", "413376", "702408", "1190808", "2014608", "3401833", "5734251", "9650312", "16216602", "27213182", "45608092", "76345851", "127656829", "213230144", "355817324", "593205284" ]
[ "nonn", "easy" ]
99
0
5
[ "A000045", "A000051", "A001629", "A006478", "A006479", "A175722" ]
[ "M2733" ]
N. J. A. Sloane
2025-02-16T08:32:30
oeisdata/seq/A006/A006478.seq
871880fa2e1a729a39ad8f9e1f047e81
A006479
From variance of Fibonacci search.
[ "0", "0", "0", "1", "5", "18", "52", "134", "318", "713", "1531", "3180", "6432", "12732", "24756", "47417", "89665", "167694", "310628", "570562", "1040226", "1883953", "3391799", "6073848", "10824096", "19204536", "33936456" ]
[ "nonn", "nice", "more" ]
32
0
5
[ "A006478", "A006479" ]
[ "M3880" ]
N. J. A. Sloane
2025-03-27T08:19:31
oeisdata/seq/A006/A006479.seq
eae4acdb1beb037d44d159a6439ca700
A006480
De Bruijn's S(3,n): (3n)!/(n!)^3.
[ "1", "6", "90", "1680", "34650", "756756", "17153136", "399072960", "9465511770", "227873431500", "5550996791340", "136526995463040", "3384731762521200", "84478098072866400", "2120572665910728000", "53494979785374631680", "1355345464406015082330", "34469858696831179429500", "879619727485803060256500", "22514366432046593564460000" ]
[ "nonn", "easy", "nice" ]
255
0
2
[ "A000897", "A000984", "A001459", "A002894", "A005809", "A006480", "A007004", "A008977", "A024486", "A050983", "A050984", "A091683", "A113424", "A161581", "A181545", "A187783", "A268545", "A268555", "A318245", "A318495" ]
[ "M4284" ]
N. J. A. Sloane
2025-03-09T10:27:02
oeisdata/seq/A006/A006480.seq
faf8ae238d1ff37b31707a24ea77d65c
A006481
Euler characteristics of polytopes.
[ "1", "2", "3", "4", "5", "11", "21", "36", "57", "127", "253", "463", "793", "1717", "3433", "6436", "11441", "24311", "48621", "92379", "167961", "352717", "705433", "1352079", "2496145", "5200301", "10400601", "20058301", "37442161" ]
[ "nonn", "nice" ]
32
1
2
[ "A006481", "A051920", "A320996" ]
[ "M0533" ]
N. J. A. Sloane
2018-10-26T13:35:33
oeisdata/seq/A006/A006481.seq
b32817e4a91b8e08ecccf27c572616b3
A006482
Euler characteristics of polytopes.
[ "1", "1", "0", "2", "5", "9", "14", "20", "69", "125", "209", "329", "923", "1715", "3002", "5004", "12869", "24309", "43757", "75581", "184755", "352715", "646645", "1144065", "2704155", "5200299", "9657699", "17383859", "40116599" ]
[ "nonn" ]
20
1
4
null
[ "M1357" ]
N. J. A. Sloane
2018-01-28T07:24:02
oeisdata/seq/A006/A006482.seq
5557c2ab6d027dc3462fb00e9410cf54
A006483
a(n) = Fibonacci(n)*2^n + 1.
[ "1", "3", "5", "17", "49", "161", "513", "1665", "5377", "17409", "56321", "182273", "589825", "1908737", "6176769", "19988481", "64684033", "209321985", "677380097", "2192048129", "7093616641", "22955425793", "74285318145", "240392339457", "777925951489", "2517421260801", "8146546327553", "26362777698305" ]
[ "nonn", "easy" ]
40
0
2
[ "A000045", "A006483", "A063727", "A087206", "A103435" ]
[ "M2502" ]
Dennis S. Kluk (mathemagician(AT)ameritech.net)
2022-10-01T16:19:05
oeisdata/seq/A006/A006483.seq
d9ace6c5f4a9aafaec1aa56e9f2b3a02
A006484
a(n) = n*(n + 1)*(n^2 - 3*n + 5)/6.
[ "0", "1", "3", "10", "30", "75", "161", "308", "540", "885", "1375", "2046", "2938", "4095", "5565", "7400", "9656", "12393", "15675", "19570", "24150", "29491", "35673", "42780", "50900", "60125", "70551", "82278", "95410", "110055", "126325", "144336", "164208", "186065", "210035", "236250", "264846", "295963", "329745", "366340" ]
[ "nonn", "easy" ]
50
0
3
[ "A000332", "A000447", "A006484", "A059722", "A100145", "A100177", "A100185", "A100188", "A100189" ]
[ "M2839" ]
Dennis S. Kluk (mathemagician(AT)ameritech.net)
2022-12-12T11:01:30
oeisdata/seq/A006/A006484.seq
fd2582b7f78ef64a63e7f056fa52bcb6
A006485
a(n) = (2^(2^n + 1) + 1)/3.
[ "3", "11", "171", "43691", "2863311531", "12297829382473034411", "226854911280625642308916404954512140971", "77194726158210796949047323339125271902179989777093709359638389338608753093291" ]
[ "nonn" ]
34
1
1
[ "A001045", "A006485", "A070969" ]
[ "M2912" ]
Dennis S. Kluk (mathemagician(AT)ameritech.net)
2023-04-03T16:14:48
oeisdata/seq/A006/A006485.seq
78bd3295313a6941e01f0a71d760d35f
A006486
a(n) = largest prime factor of n^n - 1.
[ "3", "13", "17", "71", "43", "4733", "241", "757", "9091", "1806113", "20593", "1803647", "8108731", "39225301", "6700417", "2699538733", "465841", "109912203092239643840221", "222361", "227633407", "285451051007", "1920647391913", "1134793633", "50150933101", "3574533119", "12557612956332313", "1100860153" ]
[ "nonn", "hard" ]
42
2
1
[ "A006486", "A006530", "A007571", "A048861", "A125135" ]
[ "M2938" ]
Dennis S. Kluk (mathemagician(AT)ameritech.net)
2022-09-08T08:44:34
oeisdata/seq/A006/A006486.seq
44c95929c5d494e042238664b274cfe6
A006487
Denominators of greedy Egyptian fraction for square root of 2.
[ "1", "3", "13", "253", "218201", "61323543802", "5704059172637470075854", "178059816815203395552917056787722451335939040", "227569456678536847041583520060628448125647436561262746582115170178319521793841532532509636" ]
[ "nonn" ]
50
0
2
null
[ "M2962" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:30
oeisdata/seq/A006/A006487.seq
c30c197e09314ca60622f0707ffa04aa
A006488
Numbers n such that n! has a square number of digits.
[ "0", "1", "2", "3", "7", "12", "18", "32", "59", "81", "105", "132", "228", "265", "284", "304", "367", "389", "435", "483", "508", "697", "726", "944", "1011", "1045", "1080", "1115", "1187", "1454", "1494", "1617", "1659", "1788", "1921", "2012", "2105", "2200", "2248", "2395", "2445", "2861", "2915", "3192", "3480", "3539", "3902", "3964", "4476" ]
[ "nonn", "base" ]
69
1
3
[ "A000142", "A006488", "A027868", "A034886", "A056851" ]
[ "M0830" ]
N. J. A. Sloane and Robert G. Wilson v
2025-02-16T08:32:30
oeisdata/seq/A006/A006488.seq
3eae653b3e6ac80725aa7daffabbb6ab
A006489
Numbers k such that k-6, k, and k+6 are primes.
[ "11", "13", "17", "23", "37", "47", "53", "67", "73", "103", "107", "157", "173", "233", "257", "263", "277", "353", "373", "563", "593", "607", "613", "647", "653", "733", "947", "977", "1097", "1103", "1123", "1187", "1223", "1283", "1297", "1367", "1433", "1453", "1487", "1493", "1607", "1613", "1663", "1747", "1753", "1783", "1867", "1873" ]
[ "nonn", "nice", "easy" ]
58
1
1
[ "A006489", "A006562", "A023201" ]
[ "M4770" ]
N. J. A. Sloane
2024-02-05T00:58:17
oeisdata/seq/A006/A006489.seq
866a3bae49cd7c272541ee369e7adc0f
A006490
a(1) = 1, a(2) = 0; for n > 2, a(n) = n*Fibonacci(n-2) (with the convention Fibonacci(0)=0, Fibonacci(1)=1).
[ "1", "0", "3", "4", "10", "18", "35", "64", "117", "210", "374", "660", "1157", "2016", "3495", "6032", "10370", "17766", "30343", "51680", "87801", "148830", "251758", "425064", "716425", "1205568", "2025675", "3399004", "5696122", "9534330", "15941099", "26625280", "44426877", "74062506", "123360230", "205303932", "341416205", "567353376" ]
[ "nonn" ]
42
1
3
[ "A000045", "A006490", "A119458" ]
[ "M2362" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A006/A006490.seq
a59804d2494e0c0d93fee82929e95c97
A006491
Generalized Lucas numbers.
[ "1", "0", "4", "5", "15", "28", "60", "117", "230", "440", "834", "1560", "2891", "5310", "9680", "17527", "31545", "56468", "100590", "178395", "315106", "554530", "972564", "1700400", "2964325", "5153868", "8938300", "15465497", "26700915", "46004620", "79112304", "135801105", "232715006", "398151740" ]
[ "nonn", "easy" ]
62
1
3
[ "A006490", "A006491", "A119458", "A320341" ]
[ "M3258" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A006/A006491.seq
89e063351b94d5b8d1e1ff5502f92e0c
A006492
Generalized Lucas numbers.
[ "1", "0", "5", "6", "21", "40", "93", "190", "396", "796", "1586", "3108", "6025", "11552", "21947", "41346", "77311", "143580", "265013", "486398", "888122", "1613944", "2920100", "5261880", "9445905", "16897328", "30127665", "53552190", "94915273", "167771168", "295794125", "520254094", "912962120", "1598652948" ]
[ "nonn" ]
28
3
3
null
[ "M3751" ]
N. J. A. Sloane.
2025-01-05T19:51:33
oeisdata/seq/A006/A006492.seq
92757722a757574e3d263878f39a7a93
A006493
Generalized Lucas numbers.
[ "1", "0", "6", "7", "28", "54", "135", "286", "627", "1313", "2730", "5565", "11212", "22304", "43911", "85614", "165490", "317373", "604296", "1143054", "2149074", "4017950", "7473180", "13832910", "25490115", "46774448", "85494900", "155693873", "282551856", "511101624", "921676437", "1657238030", "2971622493", "5314551351" ]
[ "nonn" ]
31
3
3
null
[ "M4063" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A006/A006493.seq
b816cb746ea7bedcf9590035d66ac383
A006494
Number of possible chess games at the end of the n-th ply plus number of games that terminate (i.e., mate) in fewer than n plies.
[ "1", "20", "400", "8902", "197281", "4865617", "119060679", "3195913043", "84999425906", "2439540533153", "69353270203366", "2097660204806910", "62855340727822758", "1981075507583376209" ]
[ "nonn", "hard", "nice", "fini", "more" ]
48
0
2
[ "A006494", "A048987", "A079485" ]
null
Ken Thompson (ken(AT)google.com)
2025-02-16T08:32:30
oeisdata/seq/A006/A006494.seq
f277e4efc1c488c4022f51064d99b263
A006495
Real part of (1 + 2*i)^n, where i is sqrt(-1).
[ "1", "1", "-3", "-11", "-7", "41", "117", "29", "-527", "-1199", "237", "6469", "11753", "-8839", "-76443", "-108691", "164833", "873121", "922077", "-2521451", "-9653287", "-6699319", "34867797", "103232189", "32125393", "-451910159", "-1064447283", "130656229", "5583548873" ]
[ "sign", "easy" ]
100
0
3
[ "A006495", "A006496", "A045873" ]
[ "M2880" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006495.seq
b2a73485819789fdc56e5374b83c08c7
A006496
Imaginary part of (1+2i)^n.
[ "0", "2", "4", "-2", "-24", "-38", "44", "278", "336", "-718", "-3116", "-2642", "10296", "33802", "16124", "-136762", "-354144", "-24478", "1721764", "3565918", "-1476984", "-20783558", "-34182196", "35553398", "242017776", "306268562", "-597551756", "-2726446322", "-2465133864", "8701963882", "29729597084", "15949374758" ]
[ "sign", "easy" ]
69
0
2
[ "A000351", "A001622", "A006495", "A006496", "A045873", "A098122" ]
[ "M0933" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006496.seq
52281e05c4a5e71a2304b63500b88b9e
A006497
a(n) = 3*a(n-1) + a(n-2) with a(0) = 2, a(1) = 3.
[ "2", "3", "11", "36", "119", "393", "1298", "4287", "14159", "46764", "154451", "510117", "1684802", "5564523", "18378371", "60699636", "200477279", "662131473", "2186871698", "7222746567", "23855111399", "78788080764", "260219353691", "859446141837", "2838557779202" ]
[ "nonn", "easy" ]
148
0
1
[ "A001622", "A006190", "A006497", "A014176", "A080039", "A098316", "A100230" ]
[ "M0910" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006497.seq
df9f4df24e192da3bb32542ade34170e
A006498
a(n) = a(n-1) + a(n-3) + a(n-4), a(0) = a(1) = a(2) = 1, a(3) = 2.
[ "1", "1", "1", "2", "4", "6", "9", "15", "25", "40", "64", "104", "169", "273", "441", "714", "1156", "1870", "3025", "4895", "7921", "12816", "20736", "33552", "54289", "87841", "142129", "229970", "372100", "602070", "974169", "1576239", "2550409", "4126648", "6677056", "10803704", "17480761", "28284465", "45765225", "74049690", "119814916" ]
[ "nonn", "easy", "nice" ]
162
0
4
[ "A000032", "A000034", "A000045", "A001654", "A003242", "A005251", "A006498", "A007598", "A027383", "A048716", "A059259", "A060945", "A074677", "A167606", "A209398", "A261041", "A273461", "A329860", "A329871" ]
[ "M1005" ]
N. J. A. Sloane
2025-03-25T09:25:07
oeisdata/seq/A006/A006498.seq
5da69ebd1dc4a6bfb0a557a4cb045d1e
A006499
Number of restricted circular combinations.
[ "1", "3", "9", "12", "16", "28", "49", "77", "121", "198", "324", "522", "841", "1363", "2209", "3572", "5776", "9348", "15129", "24477", "39601", "64078", "103684", "167762", "271441", "439203", "710649", "1149852", "1860496", "3010348", "4870849", "7881197", "12752041", "20633238", "33385284", "54018522", "87403801", "141422323", "228826129" ]
[ "nonn", "easy" ]
71
0
2
[ "A000032", "A006499", "A056594" ]
[ "M2768" ]
N. J. A. Sloane
2025-01-05T19:51:34
oeisdata/seq/A006/A006499.seq
c5de9bbd3ade5e03a61107177dbe9ade
A006500
Restricted combinations.
[ "1", "2", "4", "8", "12", "18", "27", "45", "75", "125", "200", "320", "512", "832", "1352", "2197", "3549", "5733", "9261", "14994", "24276", "39304", "63580", "102850", "166375", "269225", "435655", "704969", "1140624", "1845504", "2985984", "4831488", "7817616", "12649337", "20466953", "33116057", "53582633" ]
[ "nonn", "easy" ]
61
0
2
[ "A002524", "A002529", "A006500", "A072827", "A072850", "A072856", "A079955", "A080014" ]
[ "M1092" ]
N. J. A. Sloane.
2025-01-05T19:51:34
oeisdata/seq/A006/A006500.seq
eb7afc9f0a1ccac2ee25b4258b58c769