Datasets:
christopher
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oeis

Dataset card Data Studio Files
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Community
2
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666,262,453B
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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A005701
Number of exterior points formed by extending diagonals of n-gon in general position.
[ "3", "14", "40", "90", "175", "308", "504", "780", "1155", "1650", "2288", "3094", "4095", "5320", "6800", "8568", "10659", "13110", "15960", "19250", "23023", "27324", "32200", "37700", "43875", "50778", "58464", "66990", "76415", "86800", "98208", "110704", "124355" ]
[ "nonn", "easy" ]
32
0
1
[ "A005701", "A179898" ]
[ "M2968" ]
N. J. A. Sloane, Robert G. Wilson v
2022-09-08T08:44:33
oeisdata/seq/A005/A005701.seq
d20cc5acc7c95cad1cab1c6452a7cf79
A005702
Number of sesquirotational Kotzig factorizations.
[ "1", "1", "1", "0", "2", "2", "4", "8", "18", "120" ]
[ "nonn" ]
9
1
5
null
[ "M0332" ]
N. J. A. Sloane.
2012-03-30T16:44:48
oeisdata/seq/A005/A005702.seq
b84bd2acb2d1b115d92305aa539d05bb
A005703
Number of n-node connected graphs with at most one cycle.
[ "1", "1", "1", "2", "4", "8", "19", "44", "112", "287", "763", "2041", "5577", "15300", "42419", "118122", "330785", "929469", "2621272", "7411706", "21010378", "59682057", "169859257", "484234165", "1382567947", "3952860475", "11315775161", "32430737380", "93044797486", "267211342954", "768096496093", "2209772802169" ]
[ "nonn", "easy", "nice" ]
58
0
4
[ "A000055", "A000081", "A000088", "A000272", "A001187", "A001349", "A001429", "A002494", "A005703", "A006125", "A006129", "A006649", "A057500", "A062734", "A116508", "A129271", "A133686", "A134964", "A140636", "A140637", "A140638", "A143543", "A367862", "A367863", "A367869", "A368834", "A368951", "A369191", "A369197", "A370316", "A370317", "A370318" ]
[ "M1151" ]
N. J. A. Sloane, R. K. Guy
2025-02-16T08:32:29
oeisdata/seq/A005/A005703.seq
f2a2477e7bbf7e244686c9cd791cb35e
A005704
Number of partitions of 3n into powers of 3.
[ "1", "2", "3", "5", "7", "9", "12", "15", "18", "23", "28", "33", "40", "47", "54", "63", "72", "81", "93", "105", "117", "132", "147", "162", "180", "198", "216", "239", "262", "285", "313", "341", "369", "402", "435", "468", "508", "548", "588", "635", "682", "729", "783", "837", "891", "954", "1017", "1080", "1152", "1224", "1296", "1377", "1458", "1539", "1632" ]
[ "nonn" ]
77
0
2
[ "A000041", "A000123", "A005704", "A005705", "A005706", "A006996", "A018819" ]
[ "M0639" ]
N. J. A. Sloane
2024-01-28T12:32:01
oeisdata/seq/A005/A005704.seq
d7cb5359503e0759de6eb91ddca0a682
A005705
Number of partitions of 4*n into powers of 4.
[ "1", "2", "3", "4", "6", "8", "10", "12", "15", "18", "21", "24", "28", "32", "36", "40", "46", "52", "58", "64", "72", "80", "88", "96", "106", "116", "126", "136", "148", "160", "172", "184", "199", "214", "229", "244", "262", "280", "298", "316", "337", "358", "379", "400", "424", "448", "472", "496", "524", "552", "580", "608", "640", "672", "704", "736", "772", "808", "844" ]
[ "nonn", "easy" ]
54
0
2
[ "A000041", "A000123", "A005704", "A005705", "A005706", "A292477" ]
[ "M0552" ]
N. J. A. Sloane
2020-03-15T07:50:26
oeisdata/seq/A005/A005705.seq
c654afc19c3d5a0a8142de92734cf7b0
A005706
Number of partitions of 5n into powers of 5.
[ "1", "2", "3", "4", "5", "7", "9", "11", "13", "15", "18", "21", "24", "27", "30", "34", "38", "42", "46", "50", "55", "60", "65", "70", "75", "82", "89", "96", "103", "110", "119", "128", "137", "146", "155", "166", "177", "188", "199", "210", "223", "236", "249", "262", "275", "290", "305", "320", "335", "350", "368", "386", "404", "422", "440", "461", "482", "503", "524", "545" ]
[ "nonn", "easy" ]
57
0
2
[ "A000041", "A000123", "A005704", "A005705", "A005706", "A292477" ]
[ "M0519" ]
N. J. A. Sloane
2018-04-30T10:53:11
oeisdata/seq/A005/A005706.seq
c4d67d60180a6475f54048e653f3156b
A005707
a(1) = a(2) = a(3) = a(4) = 1, a(n) = a(a(n-1))+a(n-a(n-1)) for n >= 5.
[ "1", "1", "1", "1", "2", "2", "3", "3", "3", "4", "4", "4", "4", "5", "6", "6", "6", "6", "6", "7", "8", "8", "9", "9", "9", "9", "9", "9", "10", "11", "11", "12", "12", "12", "13", "13", "13", "13", "13", "13", "13", "14", "15", "16", "16", "17", "17", "17", "18", "18", "18", "18", "19", "19", "19", "19", "19", "19", "19", "19", "20", "21", "22", "22", "23", "24", "24", "25", "25", "25", "26", "26", "26", "26", "27", "27", "27", "27", "27" ]
[ "nonn", "easy", "nice" ]
27
1
5
[ "A004001", "A005185", "A005350", "A005707" ]
[ "M0251" ]
N. J. A. Sloane
2017-10-12T19:08:19
oeisdata/seq/A005/A005707.seq
9593061829e16c8b4a1858f0d4f24d7f
A005708
a(n) = a(n-1) + a(n-6), with a(i) = 1 for i = 0..5.
[ "1", "1", "1", "1", "1", "1", "2", "3", "4", "5", "6", "7", "9", "12", "16", "21", "27", "34", "43", "55", "71", "92", "119", "153", "196", "251", "322", "414", "533", "686", "882", "1133", "1455", "1869", "2402", "3088", "3970", "5103", "6558", "8427", "10829", "13917", "17887", "22990", "29548", "37975", "48804", "62721", "80608", "103598", "133146", "171121", "219925", "282646" ]
[ "nonn", "easy" ]
147
0
7
[ "A000045", "A000079", "A000930", "A003269", "A003520", "A005708", "A005709", "A005710", "A005711" ]
[ "M0496" ]
N. J. A. Sloane
2025-03-21T09:23:11
oeisdata/seq/A005/A005708.seq
950c0c39cf761f876db5e5a189ccf8f6
A005709
a(n) = a(n-1) + a(n-7), with a(i) = 1 for i = 0..6.
[ "1", "1", "1", "1", "1", "1", "1", "2", "3", "4", "5", "6", "7", "8", "10", "13", "17", "22", "28", "35", "43", "53", "66", "83", "105", "133", "168", "211", "264", "330", "413", "518", "651", "819", "1030", "1294", "1624", "2037", "2555", "3206", "4025", "5055", "6349", "7973", "10010", "12565", "15771", "19796", "24851" ]
[ "nonn", "easy" ]
113
0
8
[ "A000045", "A000079", "A000930", "A003269", "A003520", "A005708", "A005709", "A005710", "A005711" ]
[ "M0492" ]
N. J. A. Sloane
2025-03-21T09:25:16
oeisdata/seq/A005/A005709.seq
bf35b0fc7c668e50c37dae52ca9ad882
A005710
a(n) = a(n-1) + a(n-8), with a(i) = 1 for i = 0..7.
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "3", "4", "5", "6", "7", "8", "9", "11", "14", "18", "23", "29", "36", "44", "53", "64", "78", "96", "119", "148", "184", "228", "281", "345", "423", "519", "638", "786", "970", "1198", "1479", "1824", "2247", "2766", "3404", "4190", "5160", "6358", "7837", "9661", "11908", "14674", "18078", "22268", "27428", "33786", "41623" ]
[ "nonn", "easy" ]
125
0
9
[ "A000045", "A000079", "A000930", "A003269", "A003520", "A005708", "A005709", "A005710", "A005711" ]
[ "M0483" ]
N. J. A. Sloane
2024-09-11T00:39:31
oeisdata/seq/A005/A005710.seq
0f16b012a3a374044db06c8c7db31148
A005711
a(n) = a(n-1) + a(n-9) for n >= 9; a(n) = 1 for n=0..7; a(8) = 2.
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "12", "15", "19", "24", "30", "37", "45", "54", "64", "76", "91", "110", "134", "164", "201", "246", "300", "364", "440", "531", "641", "775", "939", "1140", "1386", "1686", "2050", "2490", "3021", "3662", "4437", "5376", "6516", "7902", "9588", "11638", "14128", "17149", "20811", "25248" ]
[ "nonn", "easy" ]
95
0
9
[ "A005710", "A005711" ]
[ "M0479" ]
N. J. A. Sloane
2023-05-25T06:58:13
oeisdata/seq/A005/A005711.seq
b1b18af869b0c87bf410b979356cc7ca
A005712
Coefficient of x^4 in expansion of (1+x+x^2)^n.
[ "1", "6", "19", "45", "90", "161", "266", "414", "615", "880", "1221", "1651", "2184", "2835", "3620", "4556", "5661", "6954", "8455", "10185", "12166", "14421", "16974", "19850", "23075", "26676", "30681", "35119", "40020", "45415", "51336", "57816", "64889", "72590", "80955", "90021", "99826", "110409", "121810", "134070" ]
[ "nonn", "easy" ]
78
2
2
[ "A000574", "A005581", "A005712", "A005714", "A005716", "A026729", "A027907", "A111808" ]
[ "M4129" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005712.seq
dd1befa63fa6518e044a453c439d2fc4
A005713
Define strings S(0)=0, S(1)=11, S(n) = S(n-1)S(n-2); iterate.
[ "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1", "1", "0", "1", "1", "1", "1", "0", "1" ]
[ "nonn", "easy", "nice" ]
55
0
1
[ "A001468", "A003849", "A005614", "A005713", "A014675", "A014677", "A123740", "A270788" ]
null
N. J. A. Sloane
2023-03-29T14:51:27
oeisdata/seq/A005/A005713.seq
3c0769948150f715f21b81a852adab3c
A005714
Coefficient of x^6 in expansion of (1+x+x^2)^n.
[ "1", "10", "45", "141", "357", "784", "1554", "2850", "4917", "8074", "12727", "19383", "28665", "41328", "58276", "80580", "109497", "146490", "193249", "251713", "324093", "412896", "520950", "651430", "807885", "994266", "1214955", "1474795", "1779121", "2133792", "2545224", "3020424", "3567025", "4193322", "4908309", "5721717" ]
[ "nonn", "easy" ]
68
3
2
[ "A000574", "A005581", "A005712", "A005714", "A005715", "A005716", "A111808" ]
[ "M4704" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005714.seq
411977489f2f32c5d471fd812e61665a
A005715
Coefficient of x^7 in expansion of (1+x+x^2)^n.
[ "4", "30", "126", "393", "1016", "2304", "4740", "9042", "16236", "27742", "45474", "71955", "110448", "165104", "241128", "344964", "484500", "669294", "910822", "1222749", "1621224", "2125200", "2756780", "3541590", "4509180", "5693454", "7133130", "8872231", "10960608", "13454496" ]
[ "nonn", "easy" ]
53
4
1
[ "A000574", "A005581", "A005712", "A005714", "A005715", "A005716", "A111808" ]
[ "M3632" ]
N. J. A. Sloane.
2025-02-16T08:32:29
oeisdata/seq/A005/A005715.seq
2fb69da57b707cfae1da4bb38efee4cb
A005716
Coefficient of x^8 in expansion of (1+x+x^2)^n.
[ "1", "15", "90", "357", "1107", "2907", "6765", "14355", "28314", "52624", "93093", "157950", "258570", "410346", "633726", "955434", "1409895", "2040885", "2903428", "4065963", "5612805", "7646925", "10293075", "13701285", "18050760", "23554206", "30462615", "39070540", "49721892", "62816292", "78816012", "98253540" ]
[ "nonn", "easy" ]
61
4
2
[ "A000574", "A005581", "A005712", "A005714", "A005715", "A005716", "A111808" ]
[ "M4975" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005716.seq
613ac15772b5ff46d922236af27fa6ba
A005717
Construct triangle in which n-th row is obtained by expanding (1 + x + x^2)^n and take the next-to-central column.
[ "1", "2", "6", "16", "45", "126", "357", "1016", "2907", "8350", "24068", "69576", "201643", "585690", "1704510", "4969152", "14508939", "42422022", "124191258", "363985680", "1067892399", "3136046298", "9217554129", "27114249960", "79818194925", "235128465026", "693085098852", "2044217638456", "6032675068061" ]
[ "nonn", "easy" ]
201
1
2
[ "A001006", "A002426", "A005043", "A005717", "A005773", "A027907", "A076540" ]
[ "M1612" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005717.seq
cd9b2c48b0884643c0df36105bdfddd3
A005718
Quadrinomial coefficients: C(2+n,n) + C(3+n,n) + C(4+n,n).
[ "3", "12", "31", "65", "120", "203", "322", "486", "705", "990", "1353", "1807", "2366", "3045", "3860", "4828", "5967", "7296", "8835", "10605", "12628", "14927", "17526", "20450", "23725", "27378", "31437", "35931", "40890", "46345", "52328", "58872", "66011", "73780", "82215", "91353", "101232", "111891", "123370", "135710", "148953", "163142", "178321", "194535" ]
[ "nonn", "easy" ]
69
0
1
[ "A005718", "A008287", "A062745", "A063421", "A071675", "A213548" ]
[ "M2918" ]
N. J. A. Sloane
2024-05-09T13:27:01
oeisdata/seq/A005/A005718.seq
3c7ecdc10862294cad995f2cd4c7b816
A005719
Quadrinomial coefficients.
[ "2", "12", "40", "101", "216", "413", "728", "1206", "1902", "2882", "4224", "6019", "8372", "11403", "15248", "20060", "26010", "33288", "42104", "52689", "65296", "80201", "97704", "118130", "141830", "169182", "200592", "236495", "277356", "323671", "375968", "434808", "500786", "574532", "656712", "748029", "849224", "961077" ]
[ "nonn" ]
33
2
1
[ "A005719", "A008287" ]
[ "M2019" ]
N. J. A. Sloane.
2023-06-28T20:42:03
oeisdata/seq/A005/A005719.seq
37d93d874ef25b160ee2f25f4476b4f0
A005720
Quadrinomial coefficients.
[ "1", "10", "44", "135", "336", "728", "1428", "2598", "4455", "7282", "11440", "17381", "25662", "36960", "52088", "72012", "97869", "130986", "172900", "225379", "290444", "370392", "467820", "585650", "727155", "895986", "1096200", "1332289", "1609210", "1932416", "2307888", "2742168", "3242393", "3816330", "4472412", "5219775" ]
[ "nonn", "easy" ]
44
2
2
[ "A005720", "A008287" ]
[ "M4702" ]
N. J. A. Sloane
2023-06-28T20:42:27
oeisdata/seq/A005/A005720.seq
d288f1f82c26ab74dfe3d60c10da3073
A005721
Central quadrinomial coefficients.
[ "1", "4", "44", "580", "8092", "116304", "1703636", "25288120", "379061020", "5724954544", "86981744944", "1327977811076", "20356299454276", "313095240079600", "4829571309488760", "74683398325804080", "1157402982351003420", "17971185794898859248" ]
[ "nonn", "easy" ]
106
0
2
[ "A002426", "A005190", "A005721", "A008287" ]
[ "M3681" ]
N. J. A. Sloane
2023-10-28T11:42:51
oeisdata/seq/A005/A005721.seq
bb15595872f4eba07b05b85fd8e21d5b
A005722
a(n) = (prime(n) - 1)^2.
[ "1", "4", "16", "36", "100", "144", "256", "324", "484", "784", "900", "1296", "1600", "1764", "2116", "2704", "3364", "3600", "4356", "4900", "5184", "6084", "6724", "7744", "9216", "10000", "10404", "11236", "11664", "12544", "15876", "16900", "18496", "19044", "21904", "22500", "24336", "26244", "27556", "29584", "31684", "32400", "36100" ]
[ "nonn", "easy" ]
32
1
2
[ "A001248", "A005597", "A005722", "A006093", "A065485", "A086242", "A095874", "A192134" ]
null
Scorpion(AT)aol.com
2024-05-08T04:18:42
oeisdata/seq/A005/A005722.seq
1a52b5c039dd60626f4274c83beb295d
A005723
Quadrinomial coefficients.
[ "1", "12", "155", "2128", "30276", "440484", "6506786", "97181760", "1463609356", "22187304112", "338118529539", "5175023913008", "79492847013100", "1224838471521240", "18922450356489780", "293003808610433280", "4546150487318508156", "70662280030419277200", "1100069396653853657564" ]
[ "nonn" ]
12
1
2
[ "A005190", "A005723" ]
[ "M4872" ]
N. J. A. Sloane.
2017-10-12T19:22:43
oeisdata/seq/A005/A005723.seq
87b4d70fa11c0a7c71e587431d58560e
A005724
Quadrinomial coefficients.
[ "3", "40", "546", "7728", "112035", "1650792", "24608948", "370084832", "5603730876", "85316186400", "1304770191802", "20029132137840", "308437355259930", "4762695514958640", "73716196036213800", "1143325208566357440", "17765127399780725316", "276484586847524844768", "4309270265307160983144" ]
[ "nonn" ]
21
1
1
[ "A005724", "A008287" ]
[ "M3148" ]
N. J. A. Sloane
2017-10-12T19:24:11
oeisdata/seq/A005/A005724.seq
ab3db04ce9b2cce5ce29ca091a5a62bb
A005725
Quadrinomial coefficients.
[ "1", "1", "3", "10", "31", "101", "336", "1128", "3823", "13051", "44803", "154518", "534964", "1858156", "6472168", "22597760", "79067375", "277164295", "973184313", "3422117190", "12049586631", "42478745781", "149915252028", "529606271560", "1872653175556", "6627147599476", "23471065878276", "83186110269928" ]
[ "nonn", "easy", "nice" ]
79
0
3
[ "A005725", "A008287", "A305161" ]
[ "M2843" ]
N. J. A. Sloane
2025-01-10T12:38:13
oeisdata/seq/A005/A005725.seq
c9d22a66a02ecb773cac2fe09127beb2
A005726
Quadrinomial coefficients.
[ "1", "2", "6", "20", "65", "216", "728", "2472", "8451", "29050", "100298", "347568", "1208220", "4211312", "14712960", "51507280", "180642391", "634551606", "2232223626", "7862669700", "27727507521", "97884558992", "345891702456", "1223358393120", "4330360551700" ]
[ "nonn", "easy" ]
35
1
2
null
[ "M1643" ]
N. J. A. Sloane
2017-10-12T19:25:16
oeisdata/seq/A005/A005726.seq
5fbc36bcadaf6d09937798077a046e91
A005727
n-th derivative of x^x at x=1. Also called Lehmer-Comtet numbers.
[ "1", "1", "2", "3", "8", "10", "54", "-42", "944", "-5112", "47160", "-419760", "4297512", "-47607144", "575023344", "-7500202920", "105180931200", "-1578296510400", "25238664189504", "-428528786243904", "7700297625889920", "-146004847062359040", "2913398154375730560", "-61031188196889482880" ]
[ "sign", "easy", "nice" ]
59
0
3
[ "A005168", "A005727", "A008296", "A176118", "A203852", "A215703", "A277537", "A293297" ]
[ "M0868" ]
N. J. A. Sloane
2023-10-27T19:44:01
oeisdata/seq/A005/A005727.seq
88e6563f46a85376cea507a1b29ec25d
A005728
Number of fractions in Farey series of order n.
[ "1", "2", "3", "5", "7", "11", "13", "19", "23", "29", "33", "43", "47", "59", "65", "73", "81", "97", "103", "121", "129", "141", "151", "173", "181", "201", "213", "231", "243", "271", "279", "309", "325", "345", "361", "385", "397", "433", "451", "475", "491", "531", "543", "585", "605", "629", "651", "697", "713", "755", "775", "807", "831", "883", "901", "941", "965" ]
[ "nonn", "easy", "nice" ]
131
0
2
[ "A002088", "A005728", "A006842", "A006843", "A049643", "A055197", "A055201" ]
[ "M0661" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005728.seq
0a90aeb1c76077bd5270d371a77a9564
A005729
a(n) is the smallest positive integer a for which there is an identity of the form a*n*x = Sum_{i=1..m} ai*gi(x)^n where a1, ..., am are in Z and g1(x), ..., gm(x) are in Z[x].
[ "1", "1", "2", "6", "2", "60", "2", "42", "6", "30", "1", "660", "3", "182", "30", "42", "2", "1020", "1", "570", "42", "22", "1", "106260", "10", "390", "6", "546", "1", "1740", "10", "1302", "66", "34", "70", "11220", "1", "1406", "78", "3990", "1", "223860", "1", "2838", "30", "46", "1", "4994220", "14", "210", "102", "390", "1", "54060", "110", "546", "798", "58", "1", "21455940" ]
[ "nonn", "nice", "easy" ]
46
1
3
[ "A005729", "A005730", "A005731" ]
[ "M1557" ]
N. J. A. Sloane
2024-03-11T01:55:45
oeisdata/seq/A005/A005729.seq
836179c4d9507ff91fbb7890c38e1749
A005730
Related to n-th powers of polynomials: factors complementary to A005731.
[ "1", "1", "1", "2", "1", "12", "1", "2", "3", "10", "1", "12", "1", "14", "15", "2", "1", "12", "1", "10", "21", "22", "1", "12", "5", "26", "3", "14", "1", "60", "1", "2", "33", "34", "35", "12", "1", "38", "39", "10", "1", "84", "1", "22", "15", "46", "1", "12", "7", "10", "51", "26", "1", "12", "55", "14", "57", "58", "1", "60", "1", "62", "21", "2", "65", "132", "1", "34", "69", "70", "1", "12", "1", "74", "15", "38", "77", "156", "1" ]
[ "nonn" ]
48
1
4
[ "A005729", "A005730", "A005731" ]
[ "M0183" ]
N. J. A. Sloane
2025-02-03T06:42:32
oeisdata/seq/A005/A005730.seq
225165c2a2ef1e01152e4af33faacd79
A005731
Related to n-th powers of polynomials: factors complementary to A005730.
[ "1", "1", "2", "3", "2", "5", "2", "21", "2", "3", "1", "55", "3", "13", "2", "21", "2", "85", "1", "57", "2", "1", "1", "8855", "2", "15", "2", "39", "1", "29", "10", "651", "2", "1", "2", "935", "1", "37", "2", "399", "1", "2665", "1", "129", "2", "1", "1", "416185", "2", "21", "2", "15", "1", "4505", "2", "39", "14", "1", "1", "357599", "1", "305", "2", "651", "6", "5", "1", "201", "2", "39", "1", "10687985", "2", "73", "2" ]
[ "nonn" ]
33
1
3
[ "A005729", "A005730", "A005731" ]
[ "M0427" ]
N. J. A. Sloane
2025-02-03T06:42:59
oeisdata/seq/A005/A005731.seq
ee3b821eecfca323f00d4c0802a359f8
A005732
a(n) = binomial(n+3,6) + binomial(n+1,5) + binomial(n,5).
[ "1", "8", "35", "111", "287", "644", "1302", "2430", "4257", "7084", "11297", "17381", "25935", "37688", "53516", "74460", "101745", "136800", "181279", "237083", "306383", "391644", "495650", "621530", "772785", "953316", "1167453", "1419985", "1716191", "2061872", "2463384", "2927672", "3462305", "4075512", "4776219", "5574087", "6479551" ]
[ "nonn", "easy", "nice" ]
58
3
2
[ "A005732", "A006600", "A007318", "A260417" ]
[ "M4514" ]
N. J. A. Sloane
2023-02-23T01:29:34
oeisdata/seq/A005/A005732.seq
6a38fad3bb5de74ceb90e7de64727fba
A005733
Least k such that binomial(k,n) has n or more distinct prime factors.
[ "2", "4", "9", "10", "22", "26", "40", "50", "54", "55", "78", "115", "123", "154", "155", "209", "288", "220", "221", "292", "301", "378", "494", "494", "551", "715", "670", "786", "805", "803", "1079", "966", "1190", "1222", "1274", "1274", "1276", "1771", "1836", "1807", "1834", "2147", "2263", "2519", "2519", "3021", "3306", "3306", "3427", "3441", "3445" ]
[ "nonn" ]
26
1
1
[ "A005733", "A005735", "A129233" ]
[ "M1166" ]
N. J. A. Sloane.
2018-05-13T10:31:07
oeisdata/seq/A005/A005733.seq
3c3afb85bce945dcbc305c408af0ee77
A005734
Incomplete version of A001049.
[ "14", "23", "28", "33", "42", "49", "59", "66", "77", "86", "96", "103", "110" ]
[ "dead" ]
5
1
1
null
null
null
1999-12-11T03:00:00
oeisdata/seq/A005/A005734.seq
cccd2883d199cd3f5d528371a58262ad
A005735
Greatest k such that binomial(k,n) has fewer than n distinct prime factors.
[ "1", "3", "8", "14", "32", "62", "87", "169", "132", "367", "389", "510", "394", "512", "512", "1880", "1880", "1882", "2099", "1879", "1885", "2102", "3470", "3470", "4805", "4806", "4806", "3475", "4806", "4938", "4939", "5108", "5119", "6271", "5122", "5869", "10663", "10663", "10663", "7421", "10667", "10667", "10668", "11710", "11711" ]
[ "nonn" ]
22
1
2
[ "A005733", "A005735", "A129233" ]
[ "M2719" ]
N. J. A. Sloane.
2017-11-11T11:53:53
oeisdata/seq/A005/A005735.seq
364e21c8c0413577243c7fd55fa270f2
A005736
Number of degenerate fanout-free Boolean functions of n variables using And, Or and Not gates.
[ "0", "2", "6", "32", "314", "4892", "104518", "2814520", "91069042", "3434371508", "147755228670", "7137203824016", "382309275191786", "22484502178536140", "1440083130444110134", "99761235465965943400", "7431676025141300550370", "592372327653418546022756" ]
[ "nonn" ]
32
0
2
[ "A005640", "A005736", "A005737", "A224766" ]
[ "M1697" ]
N. J. A. Sloane
2025-04-03T23:04:57
oeisdata/seq/A005/A005736.seq
3f5a6aab7096b2384d1f74d9560466d9
A005737
Number of fanout-free Boolean functions of n variables using And, Or and Not gates.
[ "2", "4", "14", "96", "1146", "19996", "456774", "12851768", "429005426", "16560937396", "725573492222", "35563025442192", "1927862644558314", "114519148531129036", "7397000893220477238", "516159025386346265192", "38694179227499561474786", "3101357948259644187134308" ]
[ "nonn" ]
31
0
1
[ "A005640", "A005736", "A005737", "A224766" ]
[ "M1284" ]
N. J. A. Sloane
2025-03-29T13:55:37
oeisdata/seq/A005/A005737.seq
232bc5a0e5c386e1240f5af220113264
A005738
Number of degenerate fanout-free Boolean functions of n variables using And, Or, Xor, and Not gates.
[ "0", "2", "6", "38", "526", "12022", "376430", "14821942", "700501294", "38564486966", "2421312598894", "170655141398326", "13336218401711534", "1144162670908970806", "106893046255965640174", "10800877688088297157430", "1173551859231328950561838", "136431643427143746045393718" ]
[ "nonn" ]
28
0
2
[ "A005616", "A005738", "A005739" ]
[ "M1708" ]
N. J. A. Sloane
2025-04-03T23:04:53
oeisdata/seq/A005/A005738.seq
b26ccb3ff09dfc7abc16bd460047ab44
A005739
Number of disjunctively-realizable functions of n variables.
[ "2", "4", "16", "152", "2680", "68968", "2311640", "95193064", "4645069336", "261938616104", "16756882325464", "1198897678224232", "94851206834082200", "8221740727881348520", "774839374768829174104", "78880995816162599086568", "8626562553228821851608856" ]
[ "nonn" ]
26
0
1
[ "A005616", "A005738", "A005739" ]
[ "M3531" ]
N. J. A. Sloane
2025-04-03T23:04:49
oeisdata/seq/A005/A005739.seq
bc85c36587a2ecf10202bc2e8e2ff186
A005740
Number of degenerate fanout-free Boolean functions of n variables using And, Or, Xor, Not, and Majority gates.
[ "2", "6", "38", "558", "14102", "493230", "21734582", "1150168974", "70917337622", "4987580274414", "393796969969526", "34476778683241806", "3313919458048503254", "346878958323336066222", "39271056622439364321590", "4780894577220073271485710" ]
[ "nonn" ]
25
1
1
[ "A005617", "A005740", "A005741" ]
[ "M1709" ]
N. J. A. Sloane
2025-03-29T14:13:20
oeisdata/seq/A005/A005740.seq
c0f89fb09031170260d354124ce33950
A005741
Number of fanout-free Boolean functions of n variables using And, Or, Xor, Not, and Majority gates.
[ "2", "4", "16", "160", "3112", "89488", "3358600", "154925968", "8469271816", "535078978000", "38352590740744", "3074533743260944", "272548937753080072", "26471366143068858448", "2795374966070961592072", "318874907420330435803024", "39075835592493074367768328" ]
[ "nonn" ]
32
0
1
[ "A005617", "A005740", "A005741" ]
[ "M3532" ]
N. J. A. Sloane
2025-04-04T11:09:08
oeisdata/seq/A005/A005741.seq
ed3a609caa07f0e13b4e98f639322b03
A005742
Number of degenerate fanout-free Boolean functions of n variables using And, Or, Not and Majority gates.
[ "2", "6", "32", "346", "6572", "176678", "6009040", "245551538", "11694413396", "635421164350", "38766848465336", "2622886302957962", "194847034853726140", "15763561489400425046", "1379408529039591621920", "129804134856816471241570", "13069901171127981930379940" ]
[ "nonn" ]
27
1
1
[ "A005615", "A005742", "A005743" ]
[ "M1698" ]
N. J. A. Sloane
2025-03-29T13:55:22
oeisdata/seq/A005/A005742.seq
cc77c91c523d80926fbd1976c24d2ab1
A005743
Number of fanout-free Boolean functions of n variables using And, Or, Not and Majority gates.
[ "2", "4", "14", "104", "1498", "32876", "950054", "33801424", "1426158002", "69573363284", "3851708875582", "238539414903224", "16338422029336970", "1226232142235080636", "100069553388048443990", "8822157207387535459616", "835558086134404986368866", "84609374709488540680125092" ]
[ "nonn" ]
28
0
1
[ "A005615", "A005742", "A005743" ]
[ "M3491" ]
N. J. A. Sloane
2025-04-04T01:19:37
oeisdata/seq/A005/A005743.seq
31a5a3ba82d731c995a435a3be279106
A005744
Expansion of x*(1+x-x^2)/((1-x)^4*(1+x)).
[ "0", "1", "4", "9", "17", "28", "43", "62", "86", "115", "150", "191", "239", "294", "357", "428", "508", "597", "696", "805", "925", "1056", "1199", "1354", "1522", "1703", "1898", "2107", "2331", "2570", "2825", "3096", "3384", "3689", "4012", "4353", "4713", "5092", "5491", "5910", "6350", "6811", "7294", "7799", "8327", "8878", "9453", "10052" ]
[ "nonn", "easy", "nice" ]
65
0
3
[ "A002623", "A003180", "A003453", "A005744", "A005745", "A005746", "A005747", "A005748", "A005771", "A008778", "A052265", "A181971", "A213778", "A355754" ]
[ "M3360" ]
N. J. A. Sloane, Simon Plouffe
2024-05-22T12:56:13
oeisdata/seq/A005/A005744.seq
961c3dcafa52aed8272321b18996f384
A005745
Number of n-covers of an unlabeled 3-set.
[ "1", "6", "23", "65", "156", "336", "664", "1229", "2159", "3629", "5877", "9221", "14070", "20951", "30530", "43634", "61283", "84725", "115461", "155294", "206368", "271210", "352784", "454550", "580509", "735280", "924163", "1153207", "1429292", "1760218", "2154776", "2622859", "3175555", "3825247" ]
[ "easy", "nonn" ]
22
1
2
[ "A002623", "A002727", "A005744", "A005745", "A005746", "A005747", "A005748", "A005771", "A055080", "A055609" ]
[ "M4156" ]
N. J. A. Sloane, Simon Plouffe
2023-02-28T22:25:19
oeisdata/seq/A005/A005745.seq
dc6fc2331e9f11ca5c38603854d4bd12
A005746
Number of n-covers of an unlabeled 4-set.
[ "1", "9", "51", "230", "863", "2864", "8609", "23883", "61883", "151214", "350929", "778113", "1656265", "3398229", "6743791", "12983181", "24311044", "44377016", "79124476", "138048542", "236050912", "396137492", "653285736", "1059923072", "1693592112", "2667563553", "4145373780", "6360553548", "9643151582" ]
[ "easy", "nonn" ]
35
1
2
[ "A002727", "A005744", "A005745", "A005746", "A005747", "A005748", "A005771", "A006148", "A055080", "A055082" ]
[ "M4634" ]
N. J. A. Sloane, Simon Plouffe
2023-02-28T22:25:15
oeisdata/seq/A005/A005746.seq
a1acc8380c88ee172fb139d7a7ac6cab
A005747
Number of n-covers of an unlabeled 6-set.
[ "1", "16", "196", "2197", "22952", "223034", "2004975", "16642937", "127654604", "907349654", "6000728764", "37093282121", "215296646264", "1178514299094", "6108871834312", "30098215339608", "141433252447082", "635816643771438", "2742163498527536", "11374522802412498", "45482770393453638" ]
[ "nonn" ]
22
1
2
[ "A005747", "A055080", "A055084" ]
[ "M5018" ]
N. J. A. Sloane, Simon Plouffe
2023-02-28T22:25:11
oeisdata/seq/A005/A005747.seq
643aa96f0fc604c8a95374f6310f666a
A005748
Number of n-covers of an unlabeled 7-set.
[ "1", "20", "348", "6093", "108182", "1890123", "31500927", "490890277", "7086257602", "94548676765", "1167995082810", "13406707973018", "143598707530374", "1441525802509250", "13619352767824724", "121574625625030584", "1029031775725235400", "8285521569322196569", "63648858792893665714" ]
[ "nonn" ]
22
1
2
[ "A005748", "A055080" ]
[ "M5098" ]
N. J. A. Sloane, Simon Plouffe
2023-02-28T22:25:07
oeisdata/seq/A005/A005748.seq
f6c06551affc02975421aa06d6a7ecf4
A005749
Cascade-realizable Boolean functions of n variables.
[ "4", "16", "152", "2368", "47688", "1156000", "32699080", "1057082752", "38444581640", "1553526946144", "69054999618888", "3348574955346496", "175908582307762312", "9951733002164182048", "603217074746723736776", "39001136297834245139200", "2679228986900726147063304" ]
[ "nonn" ]
28
1
1
[ "A005613", "A005749" ]
[ "M3530" ]
N. J. A. Sloane
2017-10-04T00:08:10
oeisdata/seq/A005/A005749.seq
76e25a5ac1ff78f363f55102b133d006
A005750
Number of planted matched trees with n nodes.
[ "1", "1", "3", "10", "39", "160", "702", "3177", "14830", "70678", "342860", "1686486", "8393681", "42187148", "213828802", "1091711076", "5609297942", "28982708389", "150496728594", "784952565145", "4110491658233", "21602884608167", "113907912618599", "602414753753310", "3194684310627727", "16984594260224529" ]
[ "nonn" ]
71
1
3
[ "A000151", "A005750", "A054581", "A058866", "A058870", "A245870" ]
[ "M2855" ]
N. J. A. Sloane
2025-01-13T08:22:26
oeisdata/seq/A005/A005750.seq
a21176fbb8d65e34c4da48df47941957
A005751
Number of matched trees with 2n nodes.
[ "1", "1", "2", "5", "15", "49", "180", "701", "2891", "12371", "54564", "246319", "1133602", "5300255", "25119554", "120441076", "583373822", "2851023191", "14044428996", "69677569603", "347904448580", "1747195558582", "8820848574074", "44747514381341", "228004950808983", "1166498678253839", "5990376960443432" ]
[ "nonn" ]
69
1
3
[ "A000151", "A005751", "A245870" ]
[ "M1478" ]
N. J. A. Sloane
2020-01-25T01:44:04
oeisdata/seq/A005/A005751.seq
bf3c092fef3e0f85534030ffc0a2c9ff
A005752
a(n) = n^2 + n*floor(n*tau) - floor(n*tau)^2.
[ "0", "1", "1", "5", "4", "1", "9", "5", "16", "11", "4", "19", "11", "1", "20", "9", "31", "19", "5", "31", "16", "45", "29", "11", "44", "25", "4", "41", "19", "59", "36", "11", "55", "29", "1", "49", "20", "71", "41", "9", "64", "31", "89", "55", "19", "81", "44", "5", "71", "31", "100", "59", "16", "89", "45", "121", "76", "29", "109" ]
[ "nonn" ]
26
0
4
null
null
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A005/A005752.seq
3dea1315cb693d0b47ee17d3495ac7b6
A005753
Number of rooted identity matched trees with n nodes.
[ "1", "2", "5", "18", "66", "266", "1111", "4792", "21124", "94888", "432415", "1994828", "9296712", "43706722", "207030398", "987130456", "4733961435", "22819241034", "110500644857", "537295738556", "2622248720234", "12840953621208", "63074566121245", "310693364823376", "1534374047239554", "7595642577152762" ]
[ "nonn", "eigen" ]
67
1
2
[ "A005753", "A038077", "A246312", "A255517" ]
[ "M1514" ]
N. J. A. Sloane
2020-12-26T17:31:40
oeisdata/seq/A005/A005753.seq
515d7f6cb66b66b194c210ca3f6542ad
A005754
Number of planted identity matched trees with n nodes.
[ "1", "1", "2", "7", "24", "95", "388", "1650", "7183", "31965", "144502", "662241", "3068942", "14358678", "67729973", "321759461", "1538076291", "7392775328", "35707198905", "173221206284", "843634142771", "4123376617009", "20218897206392", "99436453714990", "490355165178472", "2424146632435852" ]
[ "nonn", "nice", "easy" ]
45
1
3
[ "A005753", "A005754", "A102755", "A246312" ]
[ "M1765" ]
N. J. A. Sloane
2023-05-26T08:51:05
oeisdata/seq/A005/A005754.seq
5637019655d912abd3844ca7cb7b2c75
A005755
Number of identity matched trees with n nodes.
[ "0", "0", "0", "1", "4", "16", "64", "252", "1018", "4182", "17510", "74510", "322034", "1410362", "6251114", "27998532", "126583634", "577079333", "2650573354", "12256481666", "57021299394", "266754944481", "1254245360430", "5924659521632", "28105641930102", "133853504339029", "639801068848128" ]
[ "nonn" ]
37
1
5
[ "A005753", "A005754", "A005755", "A102755", "A246312" ]
[ "M3517" ]
N. J. A. Sloane
2020-01-25T01:44:18
oeisdata/seq/A005/A005755.seq
d1ca2f73d93d092a2e4bcbeb038770c8
A005756
Number of non-degenerate fanout-free Boolean functions of n variables having AND rank 2.
[ "4", "24", "304", "5440", "125824", "3566080", "119614464", "4633387008", "203524112384", "9995546722304", "542730361241600", "32281981804347392", "2087454641985945600", "145797871819529650176", "10938609224992417644544", "877346430770422497673216", "74913579745878635293179904", "6784650500440844952024383488" ]
[ "nonn" ]
29
2
1
[ "A005756", "A225171" ]
[ "M3607" ]
N. J. A. Sloane
2025-03-28T22:54:13
oeisdata/seq/A005/A005756.seq
9c53711ef4032186a576d9ba5eaca193
A005757
Coefficients of modular function g_4(tau).
[ "1", "14", "102", "561", "2563", "10285", "37349", "125290", "393635", "1170297", "3317941", "9025118", "23667102", "60070724", "148055380", "355322825", "832286510", "1906535024", "4278519421", "9420605029", "20378915733", "43362534963", "90852676817", "187612056437" ]
[ "nonn" ]
12
3
2
[ "A003296", "A003297", "A005757" ]
[ "M4938" ]
N. J. A. Sloane.
2020-01-13T11:28:52
oeisdata/seq/A005/A005757.seq
d6afaa6a9269c2240d79571bfb4874bd
A005758
Number of partitions of n into parts of 12 kinds.
[ "1", "12", "90", "520", "2535", "10908", "42614", "153960", "521235", "1669720", "5098938", "14931072", "42124380", "114945780", "304351020", "784087848", "1970043621", "4837060800", "11626305640", "27398234760", "63388751544", "144156086776", "322590526350" ]
[ "nonn", "easy", "nice" ]
64
0
2
[ "A005758", "A006922", "A144064" ]
[ "M4854" ]
N. J. A. Sloane, Simon Plouffe
2018-02-18T12:29:10
oeisdata/seq/A005/A005758.seq
931e145da307ab087d0af964eba0e70f
A005759
Coefficients of modular function g_6(tau).
[ "1", "19", "191", "1400", "8373", "43277", "199982", "844734", "3312600", "12197369", "42536231", "141442928", "450904486", "1384174772", "4106738807", "11812667512", "33028600519", "89972796303", "239259681221", "622181676256", "1584594241651", "3957870842872" ]
[ "nonn" ]
13
4
2
[ "A003296", "A005757", "A005759" ]
[ "M5077" ]
N. J. A. Sloane.
2020-01-13T11:29:41
oeisdata/seq/A005/A005759.seq
bdf7c747ff3711275e91c44700c3dd23
A005760
Coefficients of modular function G_2(tau).
[ "1", "2", "-12", "5", "8", "1", "7", "-11", "10", "-12", "-18", "-22", "26", "-11", "41", "44", "-15", "25", "-66", "54", "-34", "-132", "-165", "178", "-55", "189", "222", "-48", "92", "-269", "274", "-112", "-572", "-767", "756", "-209", "720", "814", "-218", "303", "-930", "1006", "-262", "-2064", "-2792", "2690", "-693", "2366", "2626", "-660", "902" ]
[ "sign", "nice" ]
16
-2
2
null
[ "M2013" ]
N. J. A. Sloane
2021-12-18T20:36:51
oeisdata/seq/A005/A005760.seq
83327dbbf5cf397f146699bd7ecbb7de
A005761
Coefficients of modular function G_3(tau).
[ "1", "-3", "-5", "24", "-13", "-22", "13", "-5", "51", "-76", "5", "102", "-12", "-64", "0", "-127", "-169", "337", "135", "466", "-806", "-234", "906", "-373", "-368", "-121", "-607", "-942", "2422", "1292", "2847", "-5294", "-1871", "5062", "-3241", "-1240", "-1089", "-2500", "-4164", "13362", "7521", "13590", "-26201", "-10290" ]
[ "sign", "nice" ]
17
-3
2
null
[ "M2507" ]
N. J. A. Sloane
2021-12-18T20:36:30
oeisdata/seq/A005/A005761.seq
8a73db96e642d0fc873f6b6ba424b48e
A005762
Coefficients of modular function G_4(tau).
[ "1", "-7", "13", "17", "-84", "57", "93", "-81", "-63", "-195", "515", "55", "-659", "236", "-153", "0", "933", "927", "-1673", "-2339", "-1108", "6542", "1520", "-6882", "3763", "-4788", "0", "7611", "6219", "-10030", "-22744", "-779", "48135", "10217", "-45495", "27389", "-48354", "-1331", "50998", "33476", "-42572" ]
[ "sign", "nice" ]
17
-4
2
[ "A005760", "A005761", "A005762" ]
[ "M4343" ]
N. J. A. Sloane
2020-01-13T11:29:25
oeisdata/seq/A005/A005762.seq
a50b6c1affbf577f5ad403075cd7584e
A005763
Exponents m_i associated with Weyl group W(E7).
[ "1", "5", "7", "9", "11", "13", "17" ]
[ "nonn", "fini", "full" ]
10
1
2
null
null
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A005/A005763.seq
b1750a24cf899c6d5d670b7623f4d34f
A005764
Coefficients of modular function denoted G_6(tau) by Atkin.
[ "1", "-5", "-13", "132", "-233", "-305", "1404", "-910", "-1533", "1382", "698", "3996", "-9363", "-1587", "14717", "-7198", "-265", "0", "-8156", "-8032", "16481", "25134", "32766", "-120680", "-33928", "206871", "-136720", "17724", "0", "8628", "58947", "-121746", "199279", "164908", "-907425" ]
[ "sign", "easy", "nice" ]
20
-6
2
[ "A005760", "A005762", "A005764" ]
[ "M3837" ]
N. J. A. Sloane
2021-12-18T20:39:03
oeisdata/seq/A005/A005764.seq
497b78c0d987ed2b361b54a3ed120d94
A005765
Size of Doehlert-Klee design with n blocks.
[ "1", "1", "3", "1", "1", "1", "7", "7", "1", "1", "11", "1", "1", "1", "15", "1", "16", "1", "19", "1", "1", "1", "23", "22", "1", "25", "27", "1", "1", "1", "31", "1", "1", "1", "35", "1", "1", "1", "39", "1", "1", "1", "43" ]
[ "nonn", "more" ]
12
2
3
null
[ "M2210" ]
N. J. A. Sloane.
2017-10-12T19:36:00
oeisdata/seq/A005/A005765.seq
f4e7d1fd7e70ca2d43093563580f27a3
A005766
a(n) = cost of minimal multiplication-cost addition chain for n.
[ "0", "1", "3", "5", "9", "12", "18", "21", "29", "34", "44", "48", "60", "67", "81", "85", "101", "110", "128", "134", "154", "165", "187", "192", "216", "229", "255", "263", "291", "306", "336", "341", "373", "390", "424", "434", "470", "489", "527", "534", "574", "595", "637", "649", "693", "716", "762", "768", "816", "841", "891", "905", "957", "984", "1038" ]
[ "nonn" ]
28
1
3
[ "A005766", "A089265" ]
[ "M2448" ]
N. J. A. Sloane, Jeffrey Shallit, Robert G. Wilson v
2019-02-28T11:47:15
oeisdata/seq/A005/A005766.seq
e48003f3a874790b304cef7d4b057b23
A005767
Solutions n to n^2 = a^2 + b^2 + c^2 (a,b,c > 0).
[ "3", "6", "7", "9", "11", "12", "13", "14", "15", "17", "18", "19", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "33", "34", "35", "36", "37", "38", "39", "41", "42", "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", "63", "65", "66", "67", "68", "69", "70", "71", "72", "73", "74", "75", "76", "77", "78", "79", "81", "82", "83", "84", "85" ]
[ "nonn", "easy" ]
28
1
1
[ "A000378", "A000408", "A000419", "A005767", "A005818", "A094958", "A169580" ]
null
N. J. A. Sloane, Ralph Peterson (ralphp(AT)library.nrl.navy.mil)
2025-02-14T15:33:54
oeisdata/seq/A005/A005767.seq
7a39560625386f56291c1d96f9c0eb86
A005768
Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex is strictly to the left of the rightmost top vertex.
[ "1", "2", "7", "27", "110", "460", "1948", "8296", "35400", "151056", "643892", "2740216", "11639416", "49340080", "208727176", "881212272", "3713043152", "15615663008", "65555425780", "274734294328", "1149506252376", "4802212126704", "20032666552664", "83452195924304", "347192769717040", "1442672957396320" ]
[ "nonn", "easy" ]
24
2
2
null
[ "M1776" ]
Simon Plouffe
2024-01-08T02:20:35
oeisdata/seq/A005/A005768.seq
090d2b67f58ba402656443194c97088d
A005769
Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex is strictly to the right of the rightmost top vertex.
[ "1", "13", "110", "758", "4617", "25895", "136949", "693369", "3395324", "16197548", "75675657", "347624505", "1574756959", "7051383905", "31266981002", "137492793602", "600295660953", "2604690331787", "11240698270037", "48279130088017", "206486210282936", "879807455701208", "3736101981855305" ]
[ "nonn", "easy" ]
26
6
2
null
[ "M4911" ]
Simon Plouffe
2024-01-08T04:34:48
oeisdata/seq/A005/A005769.seq
50de4fb953db8690c84bc31830e487c2
A005770
Number of convex polygons of length 2n on square lattice whose leftmost bottom vertex and rightmost top vertex have the same x-coordinate.
[ "1", "9", "55", "286", "1362", "6143", "26729", "113471", "473471", "1951612", "7974660", "32384127", "130926391", "527657073", "2121795391", "8518575466", "34162154550", "136893468863", "548253828965", "2194897467395", "8784784672511", "35153438973304", "140653028240520", "562719731644671" ]
[ "nonn", "easy" ]
44
5
2
[ "A005436", "A005768", "A005769", "A005770" ]
[ "M4638" ]
Simon Plouffe, N. J. A. Sloane
2024-06-04T17:08:00
oeisdata/seq/A005/A005770.seq
60455181252fa64244d1fc3b617a77bc
A005771
Number of n-covers of an unlabeled 5-set.
[ "1", "12", "103", "736", "4571", "25326", "127415", "588687", "2518997", "10053739", "37656707", "133084998", "445949359", "1422934989", "4340110439", "12697803333", "35744330644", "97081519369", "255032046536", "649459943602", "1606518048420", "3867119228081", "9073566868140", "20783186834063" ]
[ "nonn" ]
23
1
2
[ "A005771", "A006148", "A052264", "A055080", "A055083" ]
[ "M4856" ]
N. J. A. Sloane, Simon Plouffe
2023-02-28T22:25:02
oeisdata/seq/A005/A005771.seq
df0b9a81e0eea0c997cd043da6736f59
A005772
Number of permutations of length n with 2 cycle lengths.
[ "3", "14", "95", "424", "3269", "21202", "178443", "1622798", "17064179", "177093256", "2293658861", "29296367476", "416567286225", "6250052633294", "103272943796399", "1717954871163982", "32068960264609523", "601640759502181648", "12257756112146028309", "257187849583000601516" ]
[ "nonn" ]
23
3
1
[ "A005772", "A218868" ]
[ "M2978" ]
Simon Plouffe
2016-04-08T06:50:50
oeisdata/seq/A005/A005772.seq
8c0d413287671924706e24af87821fa9
A005773
Number of directed animals of size n (or directed n-ominoes in standard position).
[ "1", "1", "2", "5", "13", "35", "96", "267", "750", "2123", "6046", "17303", "49721", "143365", "414584", "1201917", "3492117", "10165779", "29643870", "86574831", "253188111", "741365049", "2173243128", "6377181825", "18730782252", "55062586341", "161995031226", "476941691177", "1405155255055", "4142457992363" ]
[ "nonn", "easy", "nice" ]
471
0
3
[ "A000108", "A001006", "A001405", "A001700", "A002426", "A005043", "A005717", "A005773", "A005775", "A026300", "A038622", "A054391", "A054392", "A054393", "A055898", "A057682", "A062105", "A064189", "A091867", "A132814", "A245455", "A295679" ]
[ "M1443" ]
N. J. A. Sloane, Simon Plouffe, Clark Kimberling
2025-01-27T11:34:16
oeisdata/seq/A005/A005773.seq
bbe94b2a0437cce3bdf31fa6f17bb105
A005774
Number of directed animals of size n (k=1 column of A038622); number of (s(0), s(1), ..., s(n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, where s(0) = 2; also sum of row n+1 of array T in A026323.
[ "0", "1", "3", "9", "26", "75", "216", "623", "1800", "5211", "15115", "43923", "127854", "372749", "1088283", "3181545", "9312312", "27287091", "80038449", "234988827", "690513030", "2030695569", "5976418602", "17601021837", "51869858544", "152951628725", "451271872701", "1332147482253" ]
[ "nonn", "easy", "nice" ]
91
0
3
[ "A005773", "A005774", "A005775", "A026010", "A038622", "A066822", "A098494" ]
[ "M2804" ]
Simon Plouffe
2021-03-12T22:32:36
oeisdata/seq/A005/A005774.seq
653dff74a06248c922b6a6da077a7b02
A005775
Number of compact-rooted directed animals of size n having 3 source points.
[ "1", "4", "14", "45", "140", "427", "1288", "3858", "11505", "34210", "101530", "300950", "891345", "2638650", "7809000", "23107488", "68375547", "202336092", "598817490", "1772479905", "5247421410", "15538054455", "46019183840", "136325212750", "403933918375", "1197131976846", "3548715207534", "10521965227669" ]
[ "nonn", "easy" ]
74
3
2
[ "A005773", "A005774", "A005775", "A038622", "A066822" ]
[ "M3481" ]
Simon Plouffe
2023-03-07T02:32:53
oeisdata/seq/A005/A005775.seq
aa2f51d1299cecdeb42195262cb74a5f
A005776
Exponents m_i associated with Weyl group W(E_8).
[ "1", "7", "11", "13", "17", "19", "23", "29" ]
[ "nonn", "fini", "full" ]
45
1
2
[ "A005556", "A005763", "A005776", "A048597", "A106373", "A106374", "A106403" ]
null
N. J. A. Sloane
2024-04-04T14:04:41
oeisdata/seq/A005/A005776.seq
4283835a27da10baf026ce17059ade2e
A005777
Rook polynomials.
[ "1", "4", "18", "96", "265", "672", "1617", "3776", "8577", "19080", "41745", "90048", "191945", "404992", "846945", "1757440", "3621697", "7417800", "15109313", "30623520", "61788489", "124158496", "248549937", "495852480", "986076225", "1955203016", "3866245425", "7625813888", "15005718153" ]
[ "nonn" ]
18
1
2
[ "A005777", "A259985" ]
[ "M3544" ]
N. J. A. Sloane.
2016-08-27T07:15:14
oeisdata/seq/A005/A005777.seq
1768854ffc6fc3af124784c16c807562
A005778
Rook polynomials.
[ "1", "9", "72", "320", "1185", "3892", "11776", "33480", "90745", "236808", "599112", "1477216", "3564001", "8439960", "19666688", "45183824", "102520881", "230046452", "511085960", "1125313056", "2457641857", "5327760940", "11471647872", "24547187800", "52225646057", "110524638672" ]
[ "nonn" ]
14
1
2
[ "A005778", "A259985" ]
[ "M4647" ]
N. J. A. Sloane.
2016-08-27T05:37:10
oeisdata/seq/A005/A005778.seq
dca14c30249e173827cfd097d9ac9a0f
A005779
a(n) = largest integer such that every tournament on n nodes contains a consistent set of n arcs.
[ "1", "2", "4", "6", "9", "12", "20", "24", "30", "35", "44", "50" ]
[ "nonn" ]
11
2
2
null
[ "M1000" ]
N. J. A. Sloane.
2012-03-30T16:44:49
oeisdata/seq/A005/A005779.seq
98574adfeed5d526c95ad9e7d26f1aea
A005780
Erroneous version of A033678.
[ "1", "0", "1", "3", "38", "680" ]
[ "dead" ]
3
1
4
null
null
null
1999-12-11T03:00:00
oeisdata/seq/A005/A005780.seq
942648bcb14b6eb5966c0bd91a8dc401
A005781
Erroneous version of A273867.
[ "2", "5", "6", "8", "9", "11" ]
[ "dead" ]
8
1
1
null
null
null
2024-12-10T06:12:21
oeisdata/seq/A005/A005781.seq
13f23eb5373ebc98666ab966ee4ce1bc
A005782
Number of n-gons in cubic curve.
[ "24", "54", "216", "648", "2376", "8100", "29232", "104544", "381672", "1397070", "5163480", "19170432", "71587080", "268423200", "1010595960", "3817704744", "14467313448", "54975424194", "209430985176", "799644248064", "3059511345864", "11728121930100", "45035998958016", "173215362539520", "667199954727936" ]
[ "nonn", "nice" ]
63
3
1
[ "A005782", "A182589" ]
[ "M5144" ]
N. J. A. Sloane
2023-01-01T04:27:39
oeisdata/seq/A005/A005782.seq
6e0ee5bca73eccddeaca9a3752f30120
A005783
Number of 3-covers of an unlabeled n-set.
[ "1", "3", "9", "23", "51", "103", "196", "348", "590", "960", "1506", "2290", "3393", "4905", "6945", "9651", "13185", "17739", "23542", "30846", "39954", "51206", "64986", "81730", "101935", "126141", "154967", "189093", "229269", "276325", "331182", "394830", "468372", "553002", "650016", "760824", "886963" ]
[ "nonn", "easy", "nice" ]
47
0
2
[ "A002620", "A002727", "A005783", "A005784", "A005785", "A005786", "A055066", "A055080" ]
[ "M2790" ]
N. J. A. Sloane
2023-02-28T21:09:35
oeisdata/seq/A005/A005783.seq
5581a3ac6607e885872b05f42ec0ac9c
A005784
Number of 4-covers of an unlabeled n-set.
[ "1", "4", "17", "65", "230", "736", "2197", "6093", "15864", "38960", "90837", "202005", "430577", "883057", "1748909", "3355213", "6252575", "11345602", "20089514", "34778306", "58964020", "98053576", "160151566", "257229974", "406739271", "633795181", "974126408", "1477999320", "2215409037", "3282874359", "4812278064" ]
[ "easy", "nonn" ]
43
0
2
[ "A002620", "A005783", "A005784", "A005785", "A005786", "A006148", "A055066", "A055080" ]
[ "M3535" ]
N. J. A. Sloane
2023-02-28T21:09:31
oeisdata/seq/A005/A005784.seq
c9af15e83cfc0d5cd19086981c5f6053
A005785
Number of 5-covers of an unlabeled n-set.
[ "1", "5", "28", "156", "863", "4571", "22952", "108182", "477136", "1969270", "7625579", "27804973", "95858868", "313747418", "978734539", "2920530663", "8363945469", "23057872913", "61357278239", "157985305473", "394486861086", "957156158394", "2260761331227" ]
[ "nonn", "easy" ]
45
0
2
[ "A002620", "A005783", "A005784", "A005785", "A052264", "A055066", "A055080" ]
[ "M3949" ]
N. J. A. Sloane
2023-02-28T21:09:28
oeisdata/seq/A005/A005785.seq
6ad99fced0371e50e1c77d78a6e5c9a9
A005786
Number of 6-covers of an unlabeled n-set.
[ "1", "6", "43", "336", "2864", "25326", "223034", "1890123", "15115098", "112980937", "787320629", "5121184083", "31188412225", "178517111561", "964196387369", "4933278065881", "23997707450765", "111358094980387", "494444748602595", "2106504840061571" ]
[ "nonn" ]
25
0
2
[ "A002620", "A005783", "A005784", "A005785", "A005786", "A055066", "A055080" ]
[ "M4244" ]
N. J. A. Sloane
2023-02-28T21:09:23
oeisdata/seq/A005/A005786.seq
45cc2142926360c5ce11bccbabcaf1b2
A005787
Reachable configurations on n circles.
[ "2", "8", "112", "5856", "869824" ]
[ "nonn", "nice", "hard", "more" ]
19
1
1
null
[ "M1904" ]
N. J. A. Sloane, Jeffrey Shallit
2020-04-30T21:40:22
oeisdata/seq/A005/A005787.seq
78c8df26ef053d4d9ebd88a72bd8e7d5
A005788
Conductors of elliptic curves.
[ "11", "14", "15", "17", "19", "20", "21", "24", "26", "27", "30", "32", "33", "34", "35", "36", "37", "38", "39", "40", "42", "43", "44", "45", "46", "48", "49", "50", "51", "52", "53", "54", "55", "56", "57", "58", "61", "62", "63", "64", "65", "66", "67", "69", "70", "72", "73", "75", "76", "77", "78" ]
[ "nonn" ]
28
1
1
[ "A005788", "A060564", "A110563", "A110620", "A217055" ]
[ "M4774" ]
N. J. A. Sloane.
2025-02-16T08:32:29
oeisdata/seq/A005/A005788.seq
f441b492f545f4ecd9de30a69bc50050
A005789
3-dimensional Catalan numbers.
[ "1", "1", "5", "42", "462", "6006", "87516", "1385670", "23371634", "414315330", "7646001090", "145862174640", "2861142656400", "57468093927120", "1178095925505960", "24584089974896430", "521086299271824330", "11198784501894470250", "243661974372798631650", "5360563436201569896300" ]
[ "nonn", "easy", "walk", "nice" ]
172
0
3
[ "A005789", "A025035", "A060854", "A268538" ]
[ "M3997" ]
N. J. A. Sloane
2024-01-02T09:37:32
oeisdata/seq/A005/A005789.seq
8810363c9290820aedda6437ae726408
A005790
4-dimensional Catalan numbers.
[ "1", "1", "14", "462", "24024", "1662804", "140229804", "13672405890", "1489877926680", "177295473274920", "22661585038594320", "3073259571003214320", "438091463242348309440", "65166105157299311029200", "10056663345892631910888600", "1602608179958939072505281850", "262708662267696303439658400600" ]
[ "nonn", "easy" ]
68
0
3
[ "A000108", "A005789", "A005790", "A005791", "A060854" ]
[ "M4954" ]
N. J. A. Sloane
2023-08-15T11:26:59
oeisdata/seq/A005/A005790.seq
4ffee016c5e9e664380faa3cca4dc189
A005791
5-dimensional Catalan numbers.
[ "1", "1", "42", "6006", "1662804", "701149020", "396499770810", "278607172289160", "231471904322784840", "219738059326729823880", "232553551737813227594400", "269396678720275351794712800", "336839101096824285057473785200", "449620757769949216266129125515200" ]
[ "nonn", "easy" ]
40
0
3
[ "A005791", "A060854" ]
[ "M5281" ]
N. J. A. Sloane.
2018-02-27T13:23:57
oeisdata/seq/A005/A005791.seq
0407a330bc02f6516470e35838405159
A005792
Positive numbers that are the sum of 2 squares or 3 times a square.
[ "1", "2", "3", "4", "5", "8", "9", "10", "12", "13", "16", "17", "18", "20", "25", "26", "27", "29", "32", "34", "36", "37", "40", "41", "45", "48", "49", "50", "52", "53", "58", "61", "64", "65", "68", "72", "73", "74", "75", "80", "81", "82", "85", "89", "90", "97", "98", "100", "101", "104", "106", "108", "109", "113", "116", "117", "121", "122", "125", "128", "130", "136", "137", "144", "145" ]
[ "nonn", "easy" ]
34
1
2
[ "A000290", "A000404", "A005792", "A033428", "A074764" ]
[ "M0529" ]
N. J. A. Sloane.
2017-10-21T16:06:38
oeisdata/seq/A005/A005792.seq
2ad74eef571140f6a7ceab558d90e934
A005793
Number of O_1^{2+}(Z)-orbits of Lorentzian modular group.
[ "1", "1", "1", "2", "1", "1", "2", "3", "2", "1", "2", "3", "1", "2", "3", "4", "2", "2", "2", "4", "2", "1", "4", "5", "2", "2", "3", "4", "2", "2", "4", "6", "2", "2", "4", "6", "1", "2", "5", "5", "3", "2", "2", "6", "3", "2", "6", "7", "3", "3", "4", "4", "2", "3", "5", "8", "2", "1", "5", "7", "2", "3", "7", "7", "3", "3", "2", "7", "3", "2", "8", "8", "2", "3", "5", "6", "3", "2", "6", "10", "4", "2", "5", "8", "2", "3", "7", "5", "4", "4", "4", "8", "2", "3", "9", "11", "2", "4", "6", "6", "4", "2", "6", "10" ]
[ "nonn" ]
44
1
4
[ "A005793", "A005794" ]
[ "M0078" ]
N. J. A. Sloane
2019-10-10T08:13:14
oeisdata/seq/A005/A005793.seq
85807581d86cd50b5b06550572557087
A005794
Number of SO_1^{2+}(Z) orbits of Lorentzian modular group.
[ "1", "1", "1", "2", "1", "1", "2", "3", "2", "1", "3", "3", "1", "2", "4", "4", "2", "2", "3", "5", "2", "1", "6", "5", "2", "3", "4", "4", "3", "2", "6", "7", "2", "2", "6", "7", "1", "3", "8", "5", "4", "2", "3", "9", "3", "2", "10", "7", "3", "4", "6", "5", "3", "4", "8", "10", "2", "1", "9", "8", "3", "4", "10", "8", "4", "4", "3", "10", "4", "2", "14", "8", "2", "5", "7", "9", "4", "2", "10", "13", "5", "2", "9", "10" ]
[ "nonn" ]
29
1
4
[ "A005793", "A005794" ]
[ "M0079" ]
N. J. A. Sloane.
2019-10-10T08:13:35
oeisdata/seq/A005/A005794.seq
0339ad6785001d05898ca3a086b1eaf3
A005795
Degrees of fundamental invariants of Weyl group W(E_7).
[ "2", "6", "8", "10", "12", "14", "18" ]
[ "nonn", "fini", "full" ]
15
1
1
[ "A005795", "A005796", "A273867" ]
null
N. J. A. Sloane
2024-12-10T05:31:09
oeisdata/seq/A005/A005795.seq
12c8ae998bb36b340a51ac999bb0fec7
A005796
Degrees of fundamental invariants of Weyl group W(E_8).
[ "2", "8", "12", "14", "18", "20", "24", "30" ]
[ "nonn", "fini", "full" ]
20
1
1
[ "A005795", "A005796", "A273867" ]
null
N. J. A. Sloane
2024-12-10T05:31:02
oeisdata/seq/A005/A005796.seq
48368c12fe2e2478f5826e6643320b8a
A005797
Expansion of Jacobi nome q in terms of parameter m/16.
[ "0", "1", "8", "84", "992", "12514", "164688", "2232200", "30920128", "435506703", "6215660600", "89668182220", "1305109502496", "19138260194422", "282441672732656", "4191287776164504", "62496081197436736", "935823746406530603", "14065763582458332888", "212122153814497767004", "3208590886304243284640" ]
[ "nonn", "easy" ]
65
0
3
[ "A002639", "A005797", "A005798", "A308835", "A308836", "A308837" ]
[ "M4561" ]
N. J. A. Sloane
2022-08-03T11:27:50
oeisdata/seq/A005/A005797.seq
b524cfb72b77d42cb67da53ae153d517
A005798
Expansion of (theta_2(q)/theta_3(q))^4/16 in powers of q.
[ "0", "1", "-8", "44", "-192", "718", "-2400", "7352", "-20992", "56549", "-145008", "356388", "-844032", "1934534", "-4306368", "9337704", "-19771392", "40965362", "-83207976", "165944732", "-325393024", "628092832", "-1194744096", "2241688744", "-4152367104", "7599231223", "-13749863984" ]
[ "sign", "easy" ]
91
0
3
[ "A001938", "A005797", "A005798", "A007248", "A029845", "A115977", "A128692" ]
[ "M4528" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005798.seq
738058cb6080c70a8788fd0988785fb3
A005799
Generalized Euler numbers of type 2^n.
[ "1", "1", "2", "10", "104", "1816", "47312", "1714000", "82285184", "5052370816", "386051862272", "35917232669440", "3996998043812864", "524203898507631616", "80011968856686405632", "14061403972845412526080", "2818858067801804443910144" ]
[ "nonn", "easy" ]
77
0
3
[ "A000364", "A000657", "A005799", "A008301", "A154283", "A210108", "A275801", "A275829" ]
[ "M1979" ]
N. J. A. Sloane, Simon Plouffe
2024-12-28T23:16:10
oeisdata/seq/A005/A005799.seq
92ace92f9456c8f61557c8162958eb1d
A005800
Generalized Euler numbers of type 3^2n.
[ "1", "2", "2248", "54103952", "9573516562048", "7512502267832874752", "19387585646491113265435648", "134942950050961684035671842506752", "2199105667698535717737352110310013698048" ]
[ "nonn", "easy" ]
16
0
2
[ "A000364", "A005800" ]
[ "M2188" ]
N. J. A. Sloane, Simon Plouffe
2018-12-01T07:58:25
oeisdata/seq/A005/A005800.seq
4efc81487cdd6c2921f1834774cc31e2