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christopher
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oeis

Dataset card Data Studio Files
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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
A003101
a(n) = Sum_{k = 1..n} (n - k + 1)^k.
[ "0", "1", "3", "8", "22", "65", "209", "732", "2780", "11377", "49863", "232768", "1151914", "6018785", "33087205", "190780212", "1150653920", "7241710929", "47454745803", "323154696184", "2282779990494", "16700904488705", "126356632390297", "987303454928972", "7957133905608836", "66071772829247409" ]
[ "nonn", "easy" ]
92
0
3
[ "A003101", "A026898", "A047970", "A051129", "A062810", "A247358", "A287215" ]
[ "M2745" ]
N. J. A. Sloane, Henry W. Gould
2024-02-09T10:07:24
oeisdata/seq/A003/A003101.seq
9c201e2a98de3f698ca5a2f12ff5eb99
A003102
Largest number divisible by all numbers < its n-th root.
[ "2", "24", "420", "27720", "720720", "36756720", "5354228880", "481880599200", "25619985190800", "10685862914126400", "876240758958364800", "113035057905629059200", "24792356033967973651200", "9690712164777231700912800", "2364533768205644535022723200", "396059406174445459616306136000" ]
[ "nonn", "nice" ]
25
1
1
null
[ "M2139" ]
N. J. A. Sloane, H. W. Gould
2017-06-14T19:19:58
oeisdata/seq/A003/A003102.seq
647c63e8a7ad8255dc8b0a3af85c6e01
A003103
Number of letters in NATO phonetic alphabet: Alpha, Bravo, Charlie, Delta, Echo, Foxtrot, Golf, Hotel, India, Juliet, Kilo, Lima, Mike, November, Oscar, Papa, Quebec, Romeo, Sierra, Tango, Uniform, Victor, Whiskey, Xray, Yankee, Zulu.
[ "5", "5", "7", "5", "4", "7", "4", "5", "5", "6", "4", "4", "4", "8", "5", "4", "6", "5", "6", "5", "7", "6", "7", "4", "6", "4" ]
[ "nonn", "word", "fini", "full" ]
25
1
1
null
null
N. J. A. Sloane
2017-06-15T10:14:26
oeisdata/seq/A003/A003103.seq
bd2cf6d9cfca5a62c05cd970b413d0c4
A003104
Number of hexagonal n-element polyominoes whose graph is a path.
[ "1", "1", "2", "4", "10", "24", "67", "182", "520", "1474", "4248", "12196", "35168", "101226", "291565", "838764", "2412033", "6929754", "19896915", "57084939" ]
[ "nonn", "more" ]
31
1
3
[ "A003104", "A323931", "A323932" ]
[ "M1208" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003104.seq
6dcd9198761e717751a4a311a936d4fa
A003105
Schur's 1926 partition theorem: number of partitions of n into parts 6n+1 or 6n-1.
[ "1", "1", "1", "1", "1", "2", "2", "3", "3", "3", "4", "5", "6", "7", "8", "9", "10", "12", "14", "16", "18", "20", "23", "26", "30", "34", "38", "42", "47", "53", "60", "67", "74", "82", "91", "102", "114", "126", "139", "153", "169", "187", "207", "228", "250", "274", "301", "331", "364", "399", "436", "476", "520", "569", "622", "679", "739", "804", "875", "953", "1038", "1128", "1224", "1327" ]
[ "nonn", "nice" ]
137
0
6
[ "A000041", "A000726", "A001651", "A003105", "A003114", "A109389", "A109697", "A132462", "A132463", "A186099", "A285219", "A304047" ]
[ "M0254" ]
N. J. A. Sloane, Herman P. Robinson
2025-02-16T08:32:27
oeisdata/seq/A003/A003105.seq
613975daae817c7c70cb0252e5efee2e
A003106
Number of partitions of n into parts 5k+2 or 5k+3.
[ "1", "0", "1", "1", "1", "1", "2", "2", "3", "3", "4", "4", "6", "6", "8", "9", "11", "12", "15", "16", "20", "22", "26", "29", "35", "38", "45", "50", "58", "64", "75", "82", "95", "105", "120", "133", "152", "167", "190", "210", "237", "261", "295", "324", "364", "401", "448", "493", "551", "604", "673", "739", "820", "899", "997", "1091", "1207", "1321", "1457", "1593", "1756", "1916", "2108", "2301" ]
[ "nonn", "nice", "easy" ]
139
0
7
[ "A003106", "A003113", "A003114", "A006141", "A047221", "A219607", "A264591", "A264592", "A264593", "A264594", "A264595" ]
[ "M0261" ]
N. J. A. Sloane, Herman P. Robinson
2025-02-16T08:32:27
oeisdata/seq/A003/A003106.seq
f7bd95f6aeacba70f3971c8a33712ff4
A003107
Number of partitions of n into Fibonacci parts (with a single type of 1).
[ "1", "1", "2", "3", "4", "6", "8", "10", "14", "17", "22", "27", "33", "41", "49", "59", "71", "83", "99", "115", "134", "157", "180", "208", "239", "272", "312", "353", "400", "453", "509", "573", "642", "717", "803", "892", "993", "1102", "1219", "1350", "1489", "1640", "1808", "1983", "2178", "2386", "2609", "2854", "3113", "3393", "3697", "4017", "4367", "4737" ]
[ "nonn", "easy" ]
82
0
3
[ "A000045", "A000119", "A003107", "A005092", "A007000", "A028290", "A102848", "A238998", "A319394" ]
[ "M0556" ]
N. J. A. Sloane, Herman P. Robinson
2023-10-29T01:43:38
oeisdata/seq/A003/A003107.seq
9ed6f1ae7742d077f59868ed997964ba
A003108
Number of partitions of n into cubes.
[ "1", "1", "1", "1", "1", "1", "1", "1", "2", "2", "2", "2", "2", "2", "2", "2", "3", "3", "3", "3", "3", "3", "3", "3", "4", "4", "4", "5", "5", "5", "5", "5", "6", "6", "6", "7", "7", "7", "7", "7", "8", "8", "8", "9", "9", "9", "9", "9", "10", "10", "10", "11", "11", "11", "12", "12", "13", "13", "13", "14", "14", "14", "15", "15", "17", "17", "17", "18", "18", "18", "19", "19", "21", "21", "21", "22", "22", "22", "23", "23", "25", "26", "26", "27", "27", "27", "28" ]
[ "nonn" ]
100
0
9
[ "A000578", "A001156", "A003108", "A037444", "A046042", "A068980", "A131799", "A218495", "A226748", "A259792", "A259793", "A279329", "A280263" ]
[ "M0209" ]
N. J. A. Sloane, Herman P. Robinson
2025-02-16T08:32:27
oeisdata/seq/A003/A003108.seq
ae1018c77f6d25331aa5086a6658722b
A003109
a(n) = number of special even permutations of 2*n+1.
[ "1", "1", "17", "117", "1413", "46389", "1211085", "47977305", "2302999889", "137682614769", "9844042388505", "832087399629125" ]
[ "nonn", "more" ]
29
1
3
[ "A003109", "A003110", "A003111" ]
[ "M5045" ]
N. J. A. Sloane
2019-05-17T16:26:45
oeisdata/seq/A003/A003109.seq
6fc07fe38e87f63c56ed313fe774ee35
A003110
a(n) = number of special odd permutations of 2*n+1.
[ "0", "2", "2", "108", "2028", "32870", "1213110", "46493784", "2310521000", "137466038346", "9842687925450", "832295357128500" ]
[ "nonn", "more" ]
30
1
2
[ "A003109", "A003110" ]
[ "M0393" ]
N. J. A. Sloane
2019-05-17T16:26:50
oeisdata/seq/A003/A003110.seq
845805c870b2718fc11bf07cd49616b3
A003111
Number of complete mappings of the cyclic group Z_{2n+1}.
[ "1", "1", "3", "19", "225", "3441", "79259", "2424195", "94471089", "4613520889", "275148653115", "19686730313955", "1664382756757625" ]
[ "nonn", "nice", "more" ]
66
0
3
[ "A003109", "A003110", "A003111", "A006204", "A006609", "A006717", "A071607", "A071608", "A071706" ]
[ "M3069" ]
N. J. A. Sloane
2023-07-22T07:06:31
oeisdata/seq/A003/A003111.seq
486536f26f8ca15edd313ca2604a97f2
A003112
Permanent of Schur's matrix of order 2n+1.
[ "1", "-3", "-5", "-105", "81", "6765", "175747", "30375", "25219857", "142901109", "4548104883", "-31152650265", "-5198937484375", "65230244418933", "-1300425712598285", "126691467546591", "868088125376401545", "-15139017417029296875" ]
[ "hard", "more", "sign" ]
61
0
2
[ "A003109", "A003110", "A003112" ]
[ "M2509" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003112.seq
9cd3484f3f37bce939ae2fbfb796efad
A003113
Coefficients in expansion of permanent of infinite tridiagonal matrix shown below.
[ "2", "1", "2", "2", "3", "3", "5", "5", "7", "8", "10", "11", "15", "16", "20", "23", "28", "31", "38", "42", "51", "57", "67", "75", "89", "99", "115", "129", "149", "166", "192", "213", "244", "272", "309", "344", "391", "433", "489", "543", "611", "676", "760", "839", "939", "1038", "1157", "1276", "1422", "1565", "1738", "1913", "2119", "2328", "2576", "2826", "3120" ]
[ "nonn" ]
36
0
1
[ "A003106", "A003113", "A003114", "A006141", "A119469", "A264591", "A264592", "A264593", "A264594", "A264595" ]
[ "M0270" ]
N. J. A. Sloane, Herman P. Robinson
2023-10-08T11:33:05
oeisdata/seq/A003/A003113.seq
c25e98ae82b29789af717d480fa004e7
A003114
Number of partitions of n into parts 5k+1 or 5k+4.
[ "1", "1", "1", "1", "2", "2", "3", "3", "4", "5", "6", "7", "9", "10", "12", "14", "17", "19", "23", "26", "31", "35", "41", "46", "54", "61", "70", "79", "91", "102", "117", "131", "149", "167", "189", "211", "239", "266", "299", "333", "374", "415", "465", "515", "575", "637", "709", "783", "871", "961", "1065", "1174", "1299", "1429", "1579", "1735", "1913", "2100", "2311", "2533", "2785" ]
[ "easy", "nonn", "nice", "changed" ]
151
0
5
[ "A003106", "A003113", "A003114", "A003116", "A006141", "A039899", "A039900", "A047209", "A127836", "A188216", "A203776", "A237981", "A264591", "A264592", "A264593", "A264594", "A264595", "A268187" ]
[ "M0266" ]
N. J. A. Sloane and Herman P. Robinson
2025-04-14T09:03:02
oeisdata/seq/A003/A003114.seq
b71bdb646a935135f38055610a79d21b
A003115
a(n) = 4^floor(n/2)*a(n-1) - a(n-2), for n >= 2, with a(0) = a(1) = 1.
[ "1", "1", "3", "11", "173", "2757", "176275", "11278843", "2887207533", "739113849605", "756849694787987", "775013348349049083", "3174453917988010255981", "13002562473065541659449093", "213033980384251916560403683731" ]
[ "nonn", "easy" ]
27
0
3
null
[ "M2913" ]
N. J. A. Sloane, Herman P. Robinson. Entry revised by N. J. A. Sloane, Jun 13 2012
2022-11-04T07:31:25
oeisdata/seq/A003/A003115.seq
33a38495cde8907d9a1210ffd4ef953d
A003116
Expansion of the reciprocal of the g.f. defining A039924.
[ "1", "1", "2", "4", "7", "13", "23", "41", "72", "127", "222", "388", "677", "1179", "2052", "3569", "6203", "10778", "18722", "32513", "56455", "98017", "170161", "295389", "512755", "890043", "1544907", "2681554", "4654417", "8078679", "14022089", "24337897", "42242732", "73319574", "127258596", "220878683" ]
[ "nonn", "nice", "easy" ]
83
0
3
[ "A003114", "A003116", "A034297", "A039924", "A168443", "A224959" ]
[ "M1068" ]
N. J. A. Sloane, Herman P. Robinson
2022-04-14T07:23:44
oeisdata/seq/A003/A003116.seq
d05d61dbb59a6b5065af6650685f76ac
A003117
Continued fraction for fifth root of 3.
[ "1", "4", "14", "2", "1", "1", "3", "2", "29", "2", "1", "7", "1", "5", "2", "1", "1", "19", "12", "77", "2", "16", "2", "1", "1", "15", "1", "1", "3", "14", "5", "1", "3", "2", "1", "1", "1", "1", "1", "1", "5", "1", "463", "1", "379", "3", "5", "3", "11", "1", "7", "7", "1", "1", "2", "1", "1", "1", "2", "1", "1", "1", "2", "1", "46", "17", "44", "1", "1", "1", "2", "24", "9", "1", "7", "4", "1", "2", "2", "1", "3", "2", "7", "1", "7", "1", "1", "2", "1", "1", "4", "1", "46", "8", "2" ]
[ "nonn", "cofr" ]
36
0
2
[ "A003117", "A005532" ]
[ "M3473" ]
N. J. A. Sloane
2024-07-05T11:10:05
oeisdata/seq/A003/A003117.seq
e36c256b7c3c4d20bc6031807be9a1ba
A003118
Continued fraction for fifth root of 4.
[ "1", "3", "7", "1", "2", "2", "1", "2", "4", "56", "1", "14", "2", "1", "1", "3", "5", "6", "2", "1", "1", "2", "1", "1", "8", "1", "2", "2", "1", "5", "1", "4", "1", "1", "3", "3", "1", "1", "3", "7", "4", "1", "10", "1", "2", "1", "8", "2", "4", "1", "1", "9", "2", "2", "2", "1", "2", "1", "1", "1", "92", "1", "26", "4", "31", "1", "2", "4", "1", "62", "8", "5", "1", "1", "1", "2", "1", "1", "63", "1", "2", "5", "4", "2", "1" ]
[ "nonn", "cofr" ]
31
0
2
[ "A003118", "A005533" ]
[ "M2607" ]
N. J. A. Sloane
2024-07-05T11:10:01
oeisdata/seq/A003/A003118.seq
b54c88b61e9e7fdd5351e021dfc7055c
A003119
High-temperature series for spin-1/2 Ising magnetic susceptibility on diamond structure.
[ "1", "4", "12", "36", "108", "324", "948", "2772", "8076", "23508", "67980", "196548", "566820", "1633956", "4697412", "13501492", "38742652", "111146820", "318390684", "911904996", "2608952940", "7463042916", "21328259716" ]
[ "nonn", "more" ]
26
0
2
[ "A002913", "A002923", "A003119", "A003220", "A007216" ]
[ "M3451" ]
N. J. A. Sloane
2024-11-14T23:49:50
oeisdata/seq/A003/A003119.seq
0e583d0888b11d66e5b8e6cbf668d444
A003120
Number of rooted trees with n nodes and omega-valency 1.
[ "1", "1", "2", "3", "7", "13", "31", "66", "159", "365", "900", "2162", "5417", "13436", "34165", "86603", "223028", "574493", "1495524", "3900055", "10246172", "26982966", "71447432", "189664782", "505605729", "1351179886", "3623051567", "9737403960", "26243202664", "70878565004" ]
[ "nonn", "nice", "easy" ]
106
1
3
[ "A003120", "A193487", "A193488", "A193489", "A193490", "A193491" ]
[ "M0836" ]
N. J. A. Sloane
2022-04-13T13:25:16
oeisdata/seq/A003/A003120.seq
16b18ed7e9ca0c6d5f86fb54e08ffd54
A003121
Strict sense ballot numbers: n candidates, k-th candidate gets k votes.
[ "1", "1", "1", "2", "12", "286", "33592", "23178480", "108995910720", "3973186258569120", "1257987096462161167200", "3830793890438041335187545600", "123051391839834932169117010215648000", "45367448380314462649742951646437285434233600", "207515126854334868747300581954534054343817468395494400" ]
[ "nonn", "nice", "easy" ]
178
0
4
[ "A000108", "A003121", "A004065", "A005118", "A007724", "A018241", "A027686", "A064049", "A064050", "A131811", "A213457", "A282698" ]
[ "M2048" ]
Colin Mallows
2024-10-14T11:26:36
oeisdata/seq/A003/A003121.seq
c66320e7512fcfd726988741c26c8a08
A003122
Number of Hamiltonian rooted triangulations with n internal nodes and 3 external nodes.
[ "1", "3", "18", "136", "1170", "10962", "109158", "1138032", "12298392", "136803060", "1558392462", "18110005704", "214056200904", "2567339253864", "31186302919290", "383088799324192", "4752646170647124", "59485067001886392", "750454803914305388", "9535654298173667520", "121954511767711578480", "1568979034333191541588", "20295073846979967634038" ]
[ "nonn" ]
40
0
2
[ "A003122", "A003123", "A005979" ]
[ "M3049" ]
N. J. A. Sloane
2017-08-21T05:52:15
oeisdata/seq/A003/A003122.seq
577522a899ecbe5083d8535f75899820
A003123
Number of Hamiltonian rooted triangulations with n internal nodes and 4 external nodes.
[ "2", "12", "92", "800", "7554", "75664", "792448", "8595120", "95895816", "1095130728", "12753454896", "151017596448", "1814135701956", "22067487234504", "271407264938656", "3370796862212944", "42230992336570032", "533252038221313888", "6781213722509638192", "86790636905453265216" ]
[ "nonn" ]
25
0
1
null
[ "M2038" ]
N. J. A. Sloane
2017-08-21T22:35:39
oeisdata/seq/A003/A003123.seq
7409a769783452f340629046a2e7c923
A003124
One of the basic cycles in the x->3x-1 (x odd) or x/2 (x even) problem.
[ "17", "50", "25", "74", "37", "110", "55", "164", "82", "41", "122", "61", "182", "91", "272", "136", "68", "34", "17", "50", "25", "74", "37", "110", "55", "164", "82", "41", "122", "61", "182", "91", "272", "136", "68", "34", "17", "50", "25", "74", "37", "110", "55", "164", "82", "41", "122", "61", "182", "91", "272", "136", "68", "34" ]
[ "nonn", "easy" ]
21
0
1
null
null
N. J. A. Sloane
2023-10-20T22:42:22
oeisdata/seq/A003/A003124.seq
aafab64add84ca0ddfbf4a6da9e9773c
A003125
Value of an urn with n balls of type -1 and n+2 balls of type +1.
[ "2", "9", "36", "142", "558", "2189", "8594", "33796", "133097", "524743", "2070466", "8177715", "32332378", "127948218", "506708043", "2007924808", "7960694208", "31576775077", "125313590701", "497543433995", "1976277486929", "7852859853208", "31214015140480", "124106224171554" ]
[ "nonn" ]
18
1
1
null
[ "M1929" ]
N. J. A. Sloane
2015-02-03T09:00:44
oeisdata/seq/A003/A003125.seq
d18cc8bf51903bf289456ce6c40fbabb
A003126
Value of an urn with n balls of type -1 and n+1 balls of type +1.
[ "1", "4", "15", "58", "226", "882", "3457", "13606", "53683", "212090", "838484", "3319596", "13159676", "52220801", "207374051", "823906473", "3274464556", "13019414133", "51790661881", "206112818880", "820583696869", "3267935428368", "13017497498243", "51863262314021" ]
[ "nonn" ]
17
1
2
[ "A003125", "A003126" ]
[ "M3501" ]
N. J. A. Sloane
2020-01-14T05:36:55
oeisdata/seq/A003/A003126.seq
ab39d6a722daa4697301677f4cb8677b
A003127
Value of an urn with n balls of type -1 and n balls of type +1.
[ "0", "1", "4", "17", "70", "282", "1136", "4583", "18457", "74131", "296945", "1190344", "4773949", "19145523", "76751393", "307503585", "1231182078", "4929075135", "19736248104", "79031964989", "316476142454", "1267191674419", "5073155081395", "20306187559891", "81265371486027" ]
[ "nonn" ]
17
1
3
null
[ "M3537" ]
N. J. A. Sloane
2015-02-03T09:00:56
oeisdata/seq/A003/A003127.seq
bb5667e7f95942645a8fd8bc0a396208
A003128
Number of driving-point impedances of an n-terminal network.
[ "0", "0", "1", "6", "31", "160", "856", "4802", "28337", "175896", "1146931", "7841108", "56089804", "418952508", "3261082917", "26403700954", "221981169447", "1934688328192", "17454004213180", "162765041827846", "1566915224106221", "15553364227949564", "159004783733999787", "1672432865100333916" ]
[ "nonn", "nice" ]
70
0
4
[ "A000110", "A000217", "A003128", "A003129", "A003130", "A005493", "A039759", "A039765", "A123158" ]
[ "M4210" ]
N. J. A. Sloane
2024-06-08T15:44:03
oeisdata/seq/A003/A003128.seq
52b7ea1dafacd84a5da6dfb8314f246f
A003129
Number of transfer impedances of an n-terminal network.
[ "0", "3", "33", "270", "2025", "14868", "109851", "827508", "6397665", "50932233", "418175274", "3542883864", "30972408558", "279287247333", "2596195945977", "24862074701208", "245091667488207", "2485294443056496", "25903024863885465", "277278282774462210" ]
[ "nonn" ]
19
2
2
[ "A003128", "A003129", "A003130" ]
[ "M3131" ]
N. J. A. Sloane
2022-11-04T13:37:28
oeisdata/seq/A003/A003129.seq
387de61cce413ba76a2a628a9271fd57
A003130
Impedances of an n-terminal network.
[ "1", "12", "157", "1750", "17446", "164108", "1505099", "13720902", "125782441", "1167813944", "11029947952", "106273227216", "1046320856673", "10537366304920", "108606982421301", "1145873284492738", "12375688888657414", "136802023177966948", "1547385154016264531" ]
[ "nonn" ]
18
2
2
[ "A003128", "A003129", "A003130" ]
[ "M4873" ]
N. J. A. Sloane
2022-11-04T22:31:23
oeisdata/seq/A003/A003130.seq
014cd22f84bc16e1295fc3dc23e7aa56
A003131
Order of Monster simple group.
[ "8", "0", "8", "0", "1", "7", "4", "2", "4", "7", "9", "4", "5", "1", "2", "8", "7", "5", "8", "8", "6", "4", "5", "9", "9", "0", "4", "9", "6", "1", "7", "1", "0", "7", "5", "7", "0", "0", "5", "7", "5", "4", "3", "6", "8", "0", "0", "0", "0", "0", "0", "0", "0", "0" ]
[ "nonn", "fini", "full", "nice", "cons" ]
25
54
1
[ "A001228", "A001379", "A002267", "A003131", "A051161", "A174670", "A174817" ]
null
N. J. A. Sloane
2024-06-14T22:31:08
oeisdata/seq/A003/A003131.seq
50c0db90cf7b6bce08a122b745f7e4c9
A003132
Sum of squares of digits of n.
[ "0", "1", "4", "9", "16", "25", "36", "49", "64", "81", "1", "2", "5", "10", "17", "26", "37", "50", "65", "82", "4", "5", "8", "13", "20", "29", "40", "53", "68", "85", "9", "10", "13", "18", "25", "34", "45", "58", "73", "90", "16", "17", "20", "25", "32", "41", "52", "65", "80", "97", "25", "26", "29", "34", "41", "50", "61", "74", "89", "106", "36", "37", "40", "45", "52", "61", "72", "85", "100", "117", "49" ]
[ "nonn", "easy", "look", "base", "nice" ]
85
0
3
[ "A000216", "A000218", "A000221", "A003132", "A003621", "A007770", "A007953", "A008460", "A008462", "A008463", "A031176", "A039943", "A051885", "A052034", "A052035", "A055017", "A076313", "A076314", "A080151", "A080709", "A099645", "A122065", "A139566", "A257588", "A332919" ]
[ "M3355" ]
N. J. A. Sloane
2023-11-05T08:44:47
oeisdata/seq/A003/A003132.seq
bb411c24fff16a8d254e6aefe02b4d3b
A003133
Order of simple Chevalley group E_8(2).
[ "3", "3", "7", "8", "0", "4", "7", "5", "3", "1", "4", "3", "6", "3", "4", "8", "0", "6", "2", "6", "1", "3", "8", "8", "1", "9", "0", "6", "1", "4", "0", "8", "5", "5", "9", "5", "0", "7", "9", "9", "9", "1", "6", "9", "2", "2", "4", "2", "4", "6", "7", "6", "5", "1", "5", "7", "6", "1", "6", "0", "9", "5", "9", "9", "0", "9", "0", "6", "8", "8", "0", "0", "0", "0", "0" ]
[ "nonn", "fini", "full", "cons" ]
14
75
1
[ "A003133", "A008868" ]
null
N. J. A. Sloane
2024-06-14T22:31:08
oeisdata/seq/A003/A003133.seq
8fdfa246460e609d62523ff7a94e63f2
A003134
Orders of Weyl groups of type E_n.
[ "51840", "2903040", "696729600" ]
[ "nonn", "fini", "full", "bref" ]
15
6
1
[ "A001217", "A003134", "A113907" ]
null
N. J. A. Sloane
2024-06-14T22:31:08
oeisdata/seq/A003/A003134.seq
c78a849c3badbe4a537cc52c7dbefe7f
A003135
n! is a nontrivial product of factorials. It is conjectured that the list is complete.
[ "9", "10", "16" ]
[ "nonn", "bref", "more", "hard" ]
23
1
1
[ "A001013", "A003135", "A034878", "A058295", "A075082", "A109095", "A109096", "A109097", "A109098" ]
null
N. J. A. Sloane
2015-12-17T02:51:21
oeisdata/seq/A003/A003135.seq
387e2511c8275910ca8e0e943eeaa044
A003136
Loeschian numbers: numbers of the form x^2 + xy + y^2; norms of vectors in A2 lattice.
[ "0", "1", "3", "4", "7", "9", "12", "13", "16", "19", "21", "25", "27", "28", "31", "36", "37", "39", "43", "48", "49", "52", "57", "61", "63", "64", "67", "73", "75", "76", "79", "81", "84", "91", "93", "97", "100", "103", "108", "109", "111", "112", "117", "121", "124", "127", "129", "133", "139", "144", "147", "148", "151", "156", "157", "163", "169", "171", "172", "175", "181", "183", "189", "192" ]
[ "core", "easy", "nonn", "nice" ]
327
1
3
[ "A003136", "A004611", "A007645", "A032766", "A034017", "A034020", "A045897", "A060428", "A088534", "A092572", "A118886", "A198726", "A198727", "A198772", "A198773", "A198774", "A198775", "A202822", "A260682" ]
[ "M2336" ]
N. J. A. Sloane
2025-03-23T07:26:57
oeisdata/seq/A003/A003136.seq
f26ddc112e84a285cdc967501b604647
A003137
Write n in base 3 and juxtapose.
[ "1", "2", "1", "0", "1", "1", "1", "2", "2", "0", "2", "1", "2", "2", "1", "0", "0", "1", "0", "1", "1", "0", "2", "1", "1", "0", "1", "1", "1", "1", "1", "2", "1", "2", "0", "1", "2", "1", "1", "2", "2", "2", "0", "0", "2", "0", "1", "2", "0", "2", "2", "1", "0", "2", "1", "1", "2", "1", "2", "2", "2", "0", "2", "2", "1", "2", "2", "2", "1", "0", "0", "0", "1", "0", "0", "1", "1", "0", "0", "2", "1", "0", "1", "0", "1", "0", "1", "1", "1", "0", "1", "2", "1", "0", "2", "0", "1", "0", "2", "1", "1", "0", "2", "2", "1" ]
[ "nonn", "base", "cons", "easy", "tabf" ]
66
1
2
[ "A003137", "A007089", "A007376", "A030190", "A030302", "A030341", "A030373", "A030548", "A030998", "A031035", "A031076", "A031219", "A033307", "A053735", "A054634", "A054635", "A077771", "A081604" ]
[ "M0040" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003137.seq
b317a17fadde8e8b38f69ab47211f2cd
A003138
Nearest integer to 24*(2^n - 1)/n.
[ "24", "36", "56", "90", "149", "252", "435", "765", "1363", "2455", "4466", "8190", "15122", "28085", "52427", "98303", "185041", "349524", "662257", "1258290", "2396744", "4575603", "8753329", "16777215", "32212254", "61946643", "119304646", "230087533" ]
[ "nonn", "easy" ]
24
1
1
[ "A003138", "A003176", "A003177", "A121056" ]
null
N. J. A. Sloane
2022-11-06T07:44:28
oeisdata/seq/A003/A003138.seq
b9e520e162a78890c5e16e0dc01f17dc
A003139
Number of coprime chains with largest member n.
[ "1", "1", "1", "1", "2", "1", "3", "1", "3", "2", "9", "1", "10", "2", "4", "3", "19", "1", "20", "2", "6", "4", "32", "1", "21", "7", "16", "7", "84", "1", "85", "9", "18", "11", "35", "3", "161", "15", "30", "6", "212", "2", "214", "15", "12", "19", "260", "3", "154", "11", "62", "31", "521", "5", "129", "19", "90", "54", "818", "2", "820", "54", "44", "57", "207", "7", "1189", "62", "147", "8", "1406" ]
[ "nonn", "nice" ]
28
1
5
[ "A003139", "A003140" ]
[ "M0129" ]
N. J. A. Sloane
2022-01-31T01:18:42
oeisdata/seq/A003/A003139.seq
131e0f75856486fb710dd7f636c6c012
A003140
Number of coprime chains with largest member prime(n).
[ "1", "1", "2", "3", "9", "10", "19", "20", "32", "84", "85", "161", "212", "214", "260", "521", "818", "820", "1189", "1406", "1415", "2005", "2375", "3351", "5698", "6122", "6141", "6600", "6623", "7270", "23993", "26735", "33686", "33753", "55735", "55750", "66498", "85117", "90310", "147374", "165450", "165479", "249822", "250176" ]
[ "nonn", "nice" ]
26
1
3
[ "A003139", "A003140" ]
[ "M0896" ]
N. J. A. Sloane
2018-12-15T14:46:17
oeisdata/seq/A003/A003140.seq
776b196e152f8e7fe78077b0079eada8
A003141
Minimal number of arcs whose reversal yields a transitive tournament.
[ "0", "0", "0", "1", "1", "3", "4", "7", "8", "12", "15", "20", "22", "28" ]
[ "hard", "more", "nonn", "nice" ]
60
0
6
[ "A001225", "A003141", "A182079" ]
[ "M2334" ]
N. J. A. Sloane
2023-02-14T02:36:53
oeisdata/seq/A003/A003141.seq
19af4229d4bfc48f8058feafb8ef0a39
A003142
Largest subset of 3 X 3 X ... X 3 cube (in n dimensions) with no 3 points collinear.
[ "0", "2", "6", "16", "43", "124", "353" ]
[ "nonn", "hard", "more" ]
24
0
2
null
[ "M1611" ]
N. J. A. Sloane
2023-10-21T01:12:17
oeisdata/seq/A003/A003142.seq
ff7489a431af8c68f19c482264d58a31
A003143
a(2*n) = floor( 17*2^n/14 ), a(2*n+1) = floor( 12*2^n/7 ).
[ "1", "1", "2", "3", "4", "6", "9", "13", "19", "27", "38", "54", "77", "109", "155", "219", "310", "438", "621", "877", "1243", "1755", "2486", "3510", "4973", "7021", "9947", "14043", "19894", "28086", "39789", "56173", "79579", "112347", "159158", "224694", "318317", "449389", "636635", "898779", "1273270", "1797558" ]
[ "nonn", "easy" ]
52
0
3
[ "A003143", "A010892", "A049347", "A077957" ]
[ "M0570" ]
N. J. A. Sloane
2022-11-06T07:46:52
oeisdata/seq/A003/A003143.seq
84447626c27c73b9b65f6af3d38a35a1
A003144
Positions of letter a in the tribonacci word abacabaabacababac... generated by a->ab, b->ac, c->a (cf. A092782).
[ "1", "3", "5", "7", "8", "10", "12", "14", "16", "18", "20", "21", "23", "25", "27", "29", "31", "32", "34", "36", "38", "40", "42", "44", "45", "47", "49", "51", "52", "54", "56", "58", "60", "62", "64", "65", "67", "69", "71", "73", "75", "76", "78", "80", "82", "84", "86", "88", "89", "91", "93", "95", "97", "99", "101", "102", "104", "106", "108", "110", "112", "113", "115", "117", "119", "121", "123", "125" ]
[ "nonn" ]
111
1
2
[ "A003144", "A003145", "A003146", "A058265", "A080843", "A092782", "A275926", "A276788", "A276793", "A276796", "A278038", "A278039" ]
[ "M2399" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003144.seq
839678a8ad6484c98e4aa60288733ffe
A003145
Positions of letter b in the tribonacci word abacabaabacababac... generated by a->ab, b->ac, c->a (cf. A092782).
[ "2", "6", "9", "13", "15", "19", "22", "26", "30", "33", "37", "39", "43", "46", "50", "53", "57", "59", "63", "66", "70", "74", "77", "81", "83", "87", "90", "94", "96", "100", "103", "107", "111", "114", "118", "120", "124", "127", "131", "134", "138", "140", "144", "147", "151", "155", "158", "162", "164", "168", "171", "175", "179", "182", "186", "188", "192", "195", "199", "202", "206", "208" ]
[ "nonn" ]
77
1
1
[ "A003144", "A003145", "A003146", "A058265", "A080843", "A092782", "A276789", "A276794", "A276797", "A276799", "A276800", "A278038", "A278040" ]
[ "M1571" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003145.seq
2c4ecf7eccd2365088019dbd8ac8c366
A003146
Positions of letter c in the tribonacci word abacabaabacababac... generated by a->ab, b->ac, c->a (cf. A092782).
[ "4", "11", "17", "24", "28", "35", "41", "48", "55", "61", "68", "72", "79", "85", "92", "98", "105", "109", "116", "122", "129", "136", "142", "149", "153", "160", "166", "173", "177", "184", "190", "197", "204", "210", "217", "221", "228", "234", "241", "247", "254", "258", "265", "271", "278", "285", "291", "298", "302", "309", "315", "322", "329", "335", "342", "346", "353", "359" ]
[ "nonn" ]
79
1
1
[ "A003144", "A003145", "A003146", "A058265", "A080843", "A092782", "A276791", "A276792", "A276798", "A276801", "A277721", "A278038", "A278041" ]
[ "M3407" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003146.seq
2a2cd71e22d09286f7dbcbad914e8b9a
A003147
Primes p with a Fibonacci primitive root g, i.e., such that g^2 = g + 1 (mod p).
[ "5", "11", "19", "31", "41", "59", "61", "71", "79", "109", "131", "149", "179", "191", "239", "241", "251", "269", "271", "311", "359", "379", "389", "409", "419", "431", "439", "449", "479", "491", "499", "569", "571", "599", "601", "631", "641", "659", "701", "719", "739", "751", "821", "839", "929", "971", "1019", "1039", "1051", "1091", "1129", "1171", "1181", "1201", "1259", "1301" ]
[ "nonn", "easy", "nice" ]
97
1
1
[ "A001175", "A003147", "A005596", "A038872", "A083701", "A106535" ]
[ "M3811" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003147.seq
cd2f9b93f80bbfc52f1d148653cb423c
A003148
a(n+1) = a(n) + 2n*(2n+1)*a(n-1), with a(0) = a(1) = 1.
[ "1", "1", "7", "27", "321", "2265", "37575", "390915", "8281665", "114610545", "2946939975", "51083368875", "1542234996225", "32192256321225", "1114841223671175", "27254953356505875", "1064057291370698625", "29845288035840902625", "1296073464766972266375", "41049997128507054562875" ]
[ "nonn", "nice", "easy" ]
65
0
3
[ "A002943", "A003148", "A046161", "A049606", "A077568", "A084543", "A091520", "A123746", "A167552", "A167565", "A167580", "A167591" ]
[ "M4389" ]
N. J. A. Sloane
2025-04-02T03:05:02
oeisdata/seq/A003/A003148.seq
4559ee2d4d52d660f1948abde612cd19
A003149
a(n) = Sum_{k=0..n} k!(n-k)!.
[ "1", "2", "5", "16", "64", "312", "1812", "12288", "95616", "840960", "8254080", "89441280", "1060369920", "13649610240", "189550368000", "2824077312000", "44927447040000", "760034451456000", "13622700994560000", "257872110354432000", "5140559166898176000", "107637093007589376000", "2361827297364885504000" ]
[ "nonn", "easy", "nice" ]
160
0
2
[ "A003149", "A006932", "A046825", "A046878", "A046879", "A052186", "A145878", "A324495", "A324496", "A324497" ]
[ "M1496" ]
N. J. A. Sloane, Henry Gould
2025-02-16T08:32:27
oeisdata/seq/A003/A003149.seq
a6864cafc3185c07208b7e27cce20b2a
A003150
Fibonomial Catalan numbers.
[ "1", "1", "3", "20", "364", "17017", "2097018", "674740506", "568965009030", "1255571292290712", "7254987185250544104", "109744478168199574282739", "4346236474244131564253156182", "450625464087974723307205504432150", "122319234225590858340579679211039433810" ]
[ "nonn", "easy", "nice" ]
75
0
3
[ "A000045", "A001622", "A003150", "A003267", "A010048", "A062073" ]
[ "M3077" ]
N. J. A. Sloane, Henry Gould
2025-02-16T08:32:27
oeisdata/seq/A003/A003150.seq
4b3fad648cb838432bf0a3e866fc2e68
A003151
Beatty sequence for 1+sqrt(2); a(n) = floor(n*(1+sqrt(2))).
[ "2", "4", "7", "9", "12", "14", "16", "19", "21", "24", "26", "28", "31", "33", "36", "38", "41", "43", "45", "48", "50", "53", "55", "57", "60", "62", "65", "67", "70", "72", "74", "77", "79", "82", "84", "86", "89", "91", "94", "96", "98", "101", "103", "106", "108", "111", "113", "115", "118", "120", "123", "125", "127", "130", "132", "135", "137", "140", "142", "144" ]
[ "nonn", "easy" ]
95
1
1
[ "A001951", "A001952", "A001954", "A003151", "A003152", "A006337", "A028982", "A080763", "A082844", "A097509", "A109250", "A159684", "A184922", "A188037", "A197878", "A215247", "A245219", "A276862", "A317204", "A341239", "A356135" ]
[ "M1033" ]
N. J. A. Sloane
2025-04-13T16:31:26
oeisdata/seq/A003/A003151.seq
e82b1244bb9d4747dc33bac11c9c0abb
A003152
A Beatty sequence: a(n) = floor(n*(1+1/sqrt(2))).
[ "1", "3", "5", "6", "8", "10", "11", "13", "15", "17", "18", "20", "22", "23", "25", "27", "29", "30", "32", "34", "35", "37", "39", "40", "42", "44", "46", "47", "49", "51", "52", "54", "56", "58", "59", "61", "63", "64", "66", "68", "69", "71", "73", "75", "76", "78", "80", "81", "83", "85", "87", "88", "90", "92", "93", "95", "97", "99", "100", "102", "104", "105", "107", "109", "110", "112", "114", "116" ]
[ "nonn", "easy" ]
66
1
2
[ "A001951", "A001952", "A001954", "A003151", "A003152", "A006337", "A028982", "A080763", "A082844", "A097509", "A109250", "A159684", "A188037", "A245219", "A276862", "A317204" ]
[ "M2392" ]
N. J. A. Sloane
2025-04-13T09:36:59
oeisdata/seq/A003/A003152.seq
87e452900b35b2ec9bf30af1ba35bf23
A003153
a(n) = integer nearest n*(1+sqrt(2)).
[ "2", "5", "7", "10", "12", "14", "17", "19", "22", "24", "27", "29", "31", "34", "36", "39", "41", "43", "46", "48", "51", "53", "56", "58", "60", "63", "65", "68", "70", "72", "75", "77", "80", "82", "84", "87", "89", "92", "94", "97", "99", "101", "104", "106", "109", "111", "113", "116", "118", "121", "123", "126", "128", "130", "133", "135", "138", "140", "142", "145" ]
[ "nonn", "easy" ]
32
1
1
null
[ "M1331" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003153.seq
eeb8a4f1756cd70016a83ccf70375b3e
A003154
Centered 12-gonal numbers, or centered dodecagonal numbers: numbers of the form 6*k*(k-1) + 1.
[ "1", "13", "37", "73", "121", "181", "253", "337", "433", "541", "661", "793", "937", "1093", "1261", "1441", "1633", "1837", "2053", "2281", "2521", "2773", "3037", "3313", "3601", "3901", "4213", "4537", "4873", "5221", "5581", "5953", "6337", "6733", "7141", "7561", "7993", "8437", "8893", "9361", "9841", "10333", "10837", "11353", "11881", "12421" ]
[ "nonn", "easy", "nice" ]
204
1
2
[ "A000217", "A001263", "A001318", "A003154", "A003215", "A005448", "A007588", "A016754", "A016946", "A032528", "A033581", "A049598", "A056827", "A146325", "A257565", "A306980" ]
[ "M4893" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003154.seq
3b28e05635e4e8cff018a8b09e843116
A003155
Number of ways to halve an n X n chessboard.
[ "1", "1", "1", "6", "15", "255", "1897", "92263", "1972653", "281035054", "17635484470", "7490694495750", "1405083604458437", "1789509008288411290" ]
[ "nonn", "nice" ]
24
1
4
[ "A003155", "A006067", "A113900", "A257952", "A271741" ]
[ "M4111" ]
N. J. A. Sloane
2022-01-31T03:03:42
oeisdata/seq/A003/A003155.seq
f204e10e713f9f0bbb49e5549a6960c3
A003156
A self-generating sequence (see Comments for definition).
[ "1", "4", "5", "6", "9", "12", "15", "16", "17", "20", "21", "22", "25", "26", "27", "30", "33", "36", "37", "38", "41", "44", "47", "48", "49", "52", "55", "58", "59", "60", "63", "64", "65", "68", "69", "70", "73", "76", "79", "80", "81", "84", "85", "86", "89", "90", "91", "94", "97", "100", "101", "102", "105", "106", "107", "110", "111", "112", "115", "118", "121", "122", "123", "126", "129", "132" ]
[ "nonn", "changed" ]
62
1
2
[ "A001511", "A003144", "A003145", "A003146", "A003156", "A003157", "A003158", "A003159", "A007413", "A007913", "A029883", "A033485", "A035263", "A036554", "A036585", "A056196", "A065882", "A065883", "A072939", "A079523", "A080426", "A088172", "A092412", "A092606" ]
[ "M3239" ]
N. J. A. Sloane
2025-04-21T08:36:56
oeisdata/seq/A003/A003156.seq
2021cfeaac08c71e2eba1f2a363659ac
A003157
A self-generating sequence (see Comments in A003156 for the definition).
[ "3", "8", "11", "14", "19", "24", "29", "32", "35", "40", "43", "46", "51", "54", "57", "62", "67", "72", "75", "78", "83", "88", "93", "96", "99", "104", "109", "114", "117", "120", "125", "128", "131", "136", "139", "142", "147", "152", "157", "160" ]
[ "nonn", "changed" ]
34
1
1
[ "A003156", "A003157", "A003158", "A010060", "A286044", "A286045" ]
[ "M2713" ]
N. J. A. Sloane
2025-04-21T08:37:00
oeisdata/seq/A003/A003157.seq
19f15dde2e42785e8e58164bfa7ccab4
A003158
A self-generating sequence (see Comments in A003156 for the definition).
[ "2", "7", "10", "13", "18", "23", "28", "31", "34", "39", "42", "45", "50", "53", "56", "61", "66", "71", "74", "77", "82", "87", "92", "95", "98", "103", "108", "113", "116", "119", "124", "127", "130", "135", "138", "141", "146", "151", "156", "159" ]
[ "nonn", "changed" ]
35
1
1
[ "A001045", "A003156", "A003157", "A003158", "A079523", "A092606" ]
[ "M1734" ]
N. J. A. Sloane
2025-04-21T08:37:04
oeisdata/seq/A003/A003158.seq
fade05ac2a74ac96f2ba9ac918075cbb
A003159
Numbers whose binary representation ends in an even number of zeros.
[ "1", "3", "4", "5", "7", "9", "11", "12", "13", "15", "16", "17", "19", "20", "21", "23", "25", "27", "28", "29", "31", "33", "35", "36", "37", "39", "41", "43", "44", "45", "47", "48", "49", "51", "52", "53", "55", "57", "59", "60", "61", "63", "64", "65", "67", "68", "69", "71", "73", "75", "76", "77", "79", "80", "81", "83", "84", "85", "87", "89", "91", "92", "93", "95", "97", "99", "100", "101", "103", "105" ]
[ "nonn", "nice", "easy", "eigen", "base" ]
217
1
2
[ "A000041", "A001285", "A003159", "A007814", "A010060", "A036554", "A174065", "A280049", "A292118" ]
[ "M2306" ]
N. J. A. Sloane, Simon Plouffe
2025-04-04T06:34:36
oeisdata/seq/A003/A003159.seq
478949ddef6202018dbea60c51b9fba5
A003160
a(1) = a(2) = 1, a(n) = n - a(a(n-1)) - a(a(n-2)).
[ "1", "1", "1", "2", "3", "4", "4", "4", "5", "5", "5", "6", "6", "6", "7", "8", "9", "9", "9", "10", "11", "12", "12", "12", "13", "14", "15", "15", "15", "16", "16", "16", "17", "17", "17", "18", "19", "20", "20", "20", "21", "21", "21", "22", "22", "22", "23", "24", "25", "25", "25", "26", "26", "26", "27", "27", "27", "28", "29", "30", "30", "30", "31", "32", "33", "33", "33", "34", "35", "36", "36", "36", "37", "37", "37", "38" ]
[ "nonn" ]
43
1
4
[ "A003156", "A003160", "A005206", "A080426", "A095774", "A095775" ]
[ "M0446" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003160.seq
2aa223fd8a6fcb158dd204ed5184f03e
A003161
A binomial coefficient sum.
[ "1", "1", "2", "9", "36", "190", "980", "5705", "33040", "204876", "1268568", "8209278", "53105976", "354331692", "2364239592", "16140234825", "110206067400", "765868074400", "5323547715200", "37525317999884", "264576141331216", "1886768082651816", "13458185494436592", "96906387191038334", "697931136204820336" ]
[ "nonn", "easy" ]
44
0
3
[ "A000108", "A001405", "A003161", "A003162", "A008315", "A129123", "A183069", "A357824", "A361887", "A361890" ]
[ "M1931" ]
N. J. A. Sloane
2023-04-06T08:33:54
oeisdata/seq/A003/A003161.seq
8cd9a07715ef8fac7e1abf39cd761316
A003162
A binomial coefficient summation.
[ "1", "1", "1", "3", "6", "19", "49", "163", "472", "1626", "5034", "17769", "57474", "206487", "688881", "2508195", "8563020", "31504240", "109492960", "406214878", "1432030036", "5349255726", "19077934506", "71672186953", "258095737156", "974311431094", "3537275250214", "13408623649893" ]
[ "nonn", "easy" ]
43
0
4
[ "A003161", "A003162", "A183069", "A361887", "A361888", "A361889", "A361890", "A361891", "A361892" ]
[ "M2597" ]
N. J. A. Sloane
2025-03-24T10:22:14
oeisdata/seq/A003/A003162.seq
02721d38fea320e0188e73ad578dd58c
A003163
Denominators of Van der Pol numbers.
[ "1", "2", "5", "20", "350", "140", "1050", "300", "57750", "38500", "250250", "45500", "2388750", "367500", "318750", "42500", "1088106250", "128012500", "960093750", "101062500", "105761906250", "10072562500", "2289218750", "199062500", "8842968750", "707437500", "51289218750" ]
[ "nonn", "frac", "nice", "easy" ]
28
0
2
[ "A003163", "A003164" ]
[ "M1534" ]
N. J. A. Sloane
2022-01-31T01:19:25
oeisdata/seq/A003/A003163.seq
26f7bb2712272acf3046fee9ed1bfd2c
A003164
Numerators of Van der Pol numbers.
[ "1", "-1", "1", "-1", "-1", "1", "1", "-1", "-37", "111", "177", "-177", "-2753", "2753", "827", "-827", "-8386459", "8386459", "28033727", "-28033727", "-14529522883", "14529522883", "1799010587", "-1799010587", "-47497385017", "47497385017", "2217167083651", "-19954503752859" ]
[ "sign", "frac", "nice", "changed" ]
31
0
9
[ "A003163", "A003164" ]
[ "M5262" ]
N. J. A. Sloane
2025-04-20T04:07:55
oeisdata/seq/A003/A003164.seq
854a9d49c927d133306efe5f21307de4
A003165
a(n) = floor(n/2) + 1 - d(n), where d(n) is the number of divisors of n.
[ "0", "0", "0", "0", "1", "0", "2", "1", "2", "2", "4", "1", "5", "4", "4", "4", "7", "4", "8", "5", "7", "8", "10", "5", "10", "10", "10", "9", "13", "8", "14", "11", "13", "14", "14", "10", "17", "16", "16", "13", "19", "14", "20", "17", "17", "20", "22", "15", "22", "20", "22", "21", "25", "20", "24", "21", "25", "26", "28", "19", "29", "28", "26", "26", "29", "26", "32", "29", "31", "28", "34", "25", "35", "34", "32" ]
[ "nonn", "easy" ]
60
1
7
[ "A000005", "A003165", "A004526", "A352620" ]
[ "M0106" ]
N. J. A. Sloane
2022-04-20T09:23:04
oeisdata/seq/A003/A003165.seq
a21283c507596b642c5281a0d3b7620e
A003166
Numbers whose square in base 2 is a palindrome.
[ "0", "1", "3", "4523", "11991", "18197", "141683", "1092489", "3168099", "6435309", "12489657", "17906499", "68301841", "295742437", "390117873", "542959199", "4770504939", "17360493407", "73798050723", "101657343993", "107137400475", "202491428745", "1615452642807", "4902182461643", "9274278357017", "12863364360297" ]
[ "base", "nonn", "hard", "nice" ]
72
1
3
[ "A002778", "A003166", "A006995", "A029983", "A262595", "A262596" ]
[ "M3181" ]
N. J. A. Sloane, R. H. Hardin
2025-02-10T20:58:03
oeisdata/seq/A003/A003166.seq
ff7a20594ebee8bcfe92a7243f17cf46
A003167
Number of n-dimensional cuboids with integral edge lengths for which volume = surface area.
[ "2", "10", "108", "2892", "270332" ]
[ "nonn", "hard", "more" ]
34
2
1
[ "A002966", "A003167" ]
null
mjzerger(AT)adams.edu
2020-01-18T07:38:14
oeisdata/seq/A003/A003167.seq
345a3138510e699dd23a84da1a47543f
A003168
Number of blobs with 2n+1 edges.
[ "1", "1", "4", "21", "126", "818", "5594", "39693", "289510", "2157150", "16348960", "125642146", "976789620", "7668465964", "60708178054", "484093913917", "3884724864390", "31348290348086", "254225828706248", "2070856216759478", "16936016649259364" ]
[ "nonn", "easy", "nice" ]
123
0
3
[ "A003168", "A003169", "A007318", "A049124", "A100327", "A102537", "A114496", "A243662", "A336573", "A361242" ]
[ "M3574" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003168.seq
78eed3bc55ce657eb4636536031031ad
A003169
Number of 2-line arrays; or number of P-graphs with 2n edges.
[ "1", "3", "14", "79", "494", "3294", "22952", "165127", "1217270", "9146746", "69799476", "539464358", "4214095612", "33218794236", "263908187100", "2110912146295", "16985386737830", "137394914285538", "1116622717709012", "9113225693455362", "74659999210200292" ]
[ "nonn", "easy" ]
78
1
2
[ "A003168", "A003169", "A100324", "A100326", "A156894" ]
[ "M2973" ]
N. J. A. Sloane
2025-01-08T13:10:13
oeisdata/seq/A003/A003169.seq
0b4f41fd32bd9b74bf6079cad5427ac0
A003170
Number of 4 X n Latin rectangles in which the first row is in order.
[ "24", "1344", "393120", "155185920", "88390995840", "69761852246016", "74175958614030336", "103657593656495554560", "186355188348102566876160", "423073240119513285788344320", "1193404222275011001999025311744", "4123706289611916312851104783171584", "17237448791456599571078045378751528960" ]
[ "nonn", "nice" ]
28
4
1
[ "A000573", "A003170" ]
[ "M5172" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A003/A003170.seq
e1847f86e8bd1c5940d0b0436ffa5c90
A003171
Negated discriminants of orders of imaginary quadratic fields with 1 class per genus (a finite sequence).
[ "3", "4", "7", "8", "11", "12", "15", "16", "19", "20", "24", "27", "28", "32", "35", "36", "40", "43", "48", "51", "52", "60", "64", "67", "72", "75", "84", "88", "91", "96", "99", "100", "112", "115", "120", "123", "132", "147", "148", "160", "163", "168", "180", "187", "192", "195", "228", "232", "235", "240", "267", "280", "288", "312", "315", "340", "352", "372", "403" ]
[ "nonn", "fini" ]
35
1
1
[ "A000926", "A003171", "A003644", "A133288" ]
[ "M2331", "N0922" ]
N. J. A. Sloane, Mira Bernstein
2019-12-03T03:22:03
oeisdata/seq/A003/A003171.seq
bac455a5c7e6ed10c0fc16851025ffe8
A003172
Q(sqrt n) is a unique factorization domain (or simple quadratic field).
[ "2", "3", "5", "6", "7", "11", "13", "14", "17", "19", "21", "22", "23", "29", "31", "33", "37", "38", "41", "43", "46", "47", "53", "57", "59", "61", "62", "67", "69", "71", "73", "77", "83", "86", "89", "93", "94", "97", "101", "103", "107", "109", "113", "118", "127", "129", "131", "133", "134", "137", "139", "141", "149", "151", "157", "158", "161", "163", "166", "167", "173", "177", "179", "181", "191", "193", "197", "199", "201" ]
[ "nonn", "nice" ]
42
1
1
[ "A003172", "A029702", "A029705", "A061574", "A218038", "A218042" ]
[ "M0618" ]
N. J. A. Sloane
2017-06-08T16:38:31
oeisdata/seq/A003/A003172.seq
940fa310103d69a3e612c863d1c9a2c5
A003173
Heegner numbers: imaginary quadratic fields with unique factorization (or class number 1).
[ "1", "2", "3", "7", "11", "19", "43", "67", "163" ]
[ "nonn", "fini", "full", "nice", "changed" ]
236
1
2
[ "A003173", "A003174", "A005847", "A014602", "A048981", "A263465" ]
[ "M0827" ]
N. J. A. Sloane
2025-04-17T12:51:22
oeisdata/seq/A003/A003173.seq
3234fba38d9966b4d0075bea1152fa47
A003174
Positive integers D such that Q[sqrt(D)] is a quadratic field which is norm-Euclidean.
[ "2", "3", "5", "6", "7", "11", "13", "17", "19", "21", "29", "33", "37", "41", "57", "73" ]
[ "fini", "nonn", "full", "nice" ]
60
1
1
[ "A003173", "A003174", "A003246", "A048981", "A187776", "A263465" ]
[ "M0619" ]
N. J. A. Sloane
2022-07-18T22:47:09
oeisdata/seq/A003/A003174.seq
0be3d61378e9d4fa74f84d9123f02e8f
A003175
Almost certainly an erroneous version of A129427.
[ "1", "2", "8", "31", "139", "724" ]
[ "dead" ]
22
0
2
[ "A003175", "A005638", "A129427" ]
[ "M1847" ]
N. J. A. Sloane, Jul 02 2015
2017-06-16T02:35:14
oeisdata/seq/A003/A003175.seq
d2f7380a18023c74882147f010ef05f0
A003176
Integer part of 24(2^n-1)/n.
[ "24", "36", "56", "90", "148", "252", "435", "765", "1362", "2455", "4466", "8190", "15121", "28085", "52427", "98302", "185041", "349524", "662257", "1258290", "2396744", "4575603", "8753329", "16777215", "32212253", "61946642", "119304646", "230087532" ]
[ "nonn" ]
23
1
1
[ "A000799", "A003138", "A003176", "A003177", "A121056" ]
null
N. J. A. Sloane
2023-08-24T12:01:45
oeisdata/seq/A003/A003176.seq
bbb6a057782e4c17ac1afb618303dc6c
A003177
a(n) = ceiling(24(2^n-1)/n).
[ "24", "36", "56", "90", "149", "252", "436", "765", "1363", "2456", "4467", "8190", "15122", "28086", "52428", "98303", "185042", "349524", "662258", "1258290", "2396744", "4575604", "8753330", "16777215", "32212254", "61946643", "119304647", "230087533" ]
[ "nonn" ]
10
1
1
[ "A003138", "A003176", "A003177", "A121056" ]
null
N. J. A. Sloane
2017-03-25T09:39:38
oeisdata/seq/A003/A003177.seq
68671f6aa6f76cbeaf319ba83a37c038
A003178
Number of indecomposable self-dual binary codes of length 2n.
[ "1", "1", "0", "0", "1", "0", "1", "1", "2", "2", "6", "8", "26", "45", "148", "457", "2523", "20786" ]
[ "nonn", "hard", "more", "nice" ]
21
0
9
[ "A003178", "A003179", "A028362", "A028363", "A106162", "A106164" ]
[ "M0356" ]
N. J. A. Sloane
2022-01-31T01:20:23
oeisdata/seq/A003/A003178.seq
4e88bde0215f5eba82bd332da67b09ba
A003179
Number of self-dual binary codes of length 2n (up to column permutation equivalence).
[ "1", "1", "1", "1", "2", "2", "3", "4", "7", "9", "16", "25", "55", "103", "261", "731", "3295", "24147", "519492" ]
[ "nonn", "hard", "more", "nice" ]
51
0
5
[ "A003178", "A003179", "A028362", "A028363", "A105685", "A106163", "A106165" ]
[ "M0289" ]
N. J. A. Sloane
2020-02-03T09:11:17
oeisdata/seq/A003/A003179.seq
63473cd540e85675c439d33dc43c7f6b
A003180
Number of equivalence classes of Boolean functions of n variables under action of symmetric group.
[ "2", "4", "12", "80", "3984", "37333248", "25626412338274304", "67516342973185974328175690087661568", "2871827610052485009904013737758920847669809829897636746529411152822140928" ]
[ "nonn", "nice" ]
90
0
1
[ "A000612", "A001146", "A003180", "A003181", "A052265", "A055621" ]
[ "M1265", "N1405" ]
N. J. A. Sloane
2022-08-22T04:01:30
oeisdata/seq/A003/A003180.seq
b0e8ad0c83384e988d8cc0fb1b426a2b
A003181
Number of P-equivalence classes of nondegenerate Boolean functions of n variables.
[ "2", "2", "8", "68", "3904", "37329264", "25626412300941056", "67516342973185974302549277749387264", "2871827610052485009904013737758920847602293486924450772201235462734479360" ]
[ "nonn" ]
41
0
1
[ "A000371", "A001146", "A003180", "A003181", "A003465", "A007537", "A055621", "A326881" ]
[ "M0378" ]
N. J. A. Sloane
2023-10-21T01:08:35
oeisdata/seq/A003/A003181.seq
8e3293a614a84021b1d80ee96e7c7be8
A003182
Dedekind numbers: inequivalent monotone Boolean functions of n or fewer variables, or antichains of subsets of an n-set.
[ "2", "3", "5", "10", "30", "210", "16353", "490013148", "1392195548889993358", "789204635842035040527740846300252680" ]
[ "nonn", "hard", "nice", "more" ]
113
0
1
[ "A000372", "A003182", "A006126", "A006602", "A007153", "A007363", "A007411", "A014466", "A046165", "A261005", "A293606", "A293993", "A304996", "A305000", "A305857", "A306007", "A306505", "A307249", "A319721", "A320449", "A321679", "A326358", "A326363" ]
[ "M0729" ]
N. J. A. Sloane
2025-02-19T11:20:53
oeisdata/seq/A003/A003182.seq
039542d2534b8525de94cf31cf79c2d1
A003183
Number of NPN-equivalence classes of unate Boolean functions of n or fewer variables.
[ "1", "2", "3", "6", "17", "112", "8282" ]
[ "nonn", "more" ]
27
0
2
[ "A003183", "A006602", "A120587", "A120608" ]
[ "M0814" ]
N. J. A. Sloane
2023-10-21T06:34:58
oeisdata/seq/A003/A003183.seq
bc4241e01e6fc4263b7af3b7433ac762
A003184
Number of NP-equivalence classes of self-dual threshold functions of exactly n variables.
[ "1", "0", "1", "1", "4", "14", "114", "2335", "172958", "52805196" ]
[ "nonn", "more" ]
55
1
5
[ "A000619", "A001532", "A002077", "A002080", "A003184" ]
[ "M3492" ]
N. J. A. Sloane
2023-10-27T03:42:34
oeisdata/seq/A003/A003184.seq
febda04e1d2db5d685dcb44441d85d92
A003185
a(n) = (4*n+1)*(4*n+5).
[ "5", "45", "117", "221", "357", "525", "725", "957", "1221", "1517", "1845", "2205", "2597", "3021", "3477", "3965", "4485", "5037", "5621", "6237", "6885", "7565", "8277", "9021", "9797", "10605", "11445", "12317", "13221", "14157", "15125", "16125", "17157", "18221" ]
[ "nonn", "easy" ]
54
0
1
[ "A001513", "A003185", "A063164", "A078371" ]
null
N. J. A. Sloane
2023-10-08T04:44:33
oeisdata/seq/A003/A003185.seq
529b4dc0c72bafa2779254b549b8337c
A003186
Number of positive pseudo-threshold functions.
[ "3", "5", "10", "30", "198" ]
[ "nonn", "more" ]
17
1
1
null
[ "M2468" ]
N. J. A. Sloane
2023-10-21T16:54:56
oeisdata/seq/A003/A003186.seq
446eaa6db684b78a735b060b86ccfe52
A003187
Number of positive threshold functions of n variables.
[ "3", "5", "10", "27", "119" ]
[ "nonn", "more" ]
29
1
1
[ "A003187", "A132183" ]
[ "M2467" ]
N. J. A. Sloane
2023-10-21T16:55:42
oeisdata/seq/A003/A003187.seq
86b4c49849732487cb8fbbbfaea00dc9
A003188
Decimal equivalent of Gray code for n.
[ "0", "1", "3", "2", "6", "7", "5", "4", "12", "13", "15", "14", "10", "11", "9", "8", "24", "25", "27", "26", "30", "31", "29", "28", "20", "21", "23", "22", "18", "19", "17", "16", "48", "49", "51", "50", "54", "55", "53", "52", "60", "61", "63", "62", "58", "59", "57", "56", "40", "41", "43", "42", "46", "47", "45", "44", "36", "37", "39", "38", "34", "35", "33", "32", "96", "97", "99", "98", "102", "103", "101" ]
[ "nonn", "nice", "easy", "look" ]
182
0
3
[ "A003188", "A003714", "A006068", "A014550", "A038554", "A048641", "A048642", "A048724", "A055975", "A065621" ]
[ "M2250" ]
N. J. A. Sloane
2024-04-22T21:00:33
oeisdata/seq/A003/A003188.seq
5bc11d3e69434d1e8672103a214b2ef9
A003189
Erroneous version of A051240.
[ "1", "1", "1", "2", "6", "156", "7013488", "29288387523484992", "234431745534048922731115019069056" ]
[ "dead" ]
18
1
4
null
null
null
2019-10-14T04:29:36
oeisdata/seq/A003/A003189.seq
553584ce4bb5f50847006d68dee45252
A003190
Number of connected 2-plexes.
[ "1", "0", "1", "3", "29", "2101", "7011181", "1788775603301", "53304526022885278403", "366299663378889804782330207902", "1171638318502622784366970315262493034215728", "3517726593606524901243694560022510194169866584119717555335" ]
[ "nonn", "nice" ]
30
1
4
[ "A000665", "A003190", "A025035", "A125791", "A289837", "A301922", "A301924", "A302374", "A302394", "A306017", "A319540", "A320395", "A322451", "A323292", "A323299" ]
[ "M3121" ]
N. J. A. Sloane
2019-08-27T10:43:56
oeisdata/seq/A003/A003190.seq
2d6c706a72f97a44b63438f7e6ab11c4
A003191
Number of symmetric Latin squares of order 2n with constant diagonal.
[ "1", "1", "6", "5972", "1225533120" ]
[ "nonn", "hard", "nice" ]
15
1
3
null
[ "M4318" ]
N. J. A. Sloane
2022-01-31T01:20:35
oeisdata/seq/A003/A003191.seq
b317ae8ae9da067171b58d1122d97709
A003192
Length of uncrossed knight's path on an n X n board.
[ "0", "0", "2", "5", "10", "17", "24", "35", "47" ]
[ "nonn", "walk", "nice", "more", "hard" ]
69
1
3
[ "A003192", "A157416" ]
[ "M1369" ]
N. J. A. Sloane
2025-02-16T08:32:27
oeisdata/seq/A003/A003192.seq
eb58f8669b8a75b18dbb373ce375cc3a
A003193
Magnetization for body-centered cubic lattice.
[ "1", "0", "0", "0", "-2", "0", "0", "-16", "18", "0", "-168", "384", "-314", "-1632", "6264", "-9744", "-10014", "86976", "-205344", "80176", "1009338", "-3579568", "4575296", "8301024", "-54012882", "112640896", "-5164464", "-694845120", "2160781086" ]
[ "sign", "nice" ]
25
0
5
[ "A002925", "A002929", "A003193", "A003194", "A003196" ]
[ "M0015" ]
N. J. A. Sloane
2023-03-06T20:36:26
oeisdata/seq/A003/A003193.seq
48ec43929d929541ddeefda047f16f59
A003194
Susceptibility series for b.c.c. lattice.
[ "0", "0", "0", "4", "0", "0", "0", "-8", "0", "112", "-256", "156", "896", "-3536", "5472", "5400", "-49088", "115008", "-47776", "-555492", "1976736", "-2563424", "-4446272", "29452776", "-61952896", "4795392", "374024448", "-1173895476" ]
[ "sign", "nice", "more" ]
18
1
4
null
[ "M3185" ]
N. J. A. Sloane
2019-01-14T09:40:30
oeisdata/seq/A003/A003194.seq
caaee913d67790bd9d61a753c23dd773
A003195
Susceptibility series for diamond.
[ "0", "4", "0", "16", "0", "64", "96", "488", "1392", "5064", "17856", "65576", "231728", "863664", "3313392" ]
[ "nonn", "more" ]
20
1
2
[ "A003195", "A007216" ]
[ "M3191" ]
N. J. A. Sloane
2023-10-21T23:56:02
oeisdata/seq/A003/A003195.seq
843cf39241c22d5aede00579d3796c24
A003196
Magnetization series for face-centered cubic lattice.
[ "1", "0", "0", "0", "0", "0", "-2", "0", "0", "0", "0", "-24", "26", "0", "0", "-48", "-252", "720", "-438", "-192", "-984", "-1008", "12924", "-19536", "3062", "-8280", "26694", "153536", "-507948", "406056", "-79532", "729912", "631608", "-9279376", "15771600", "-7467336", "10935114", "-21835524", "-112752684", "400576168", "-410287368" ]
[ "sign", "nice" ]
22
0
7
[ "A003193", "A003196" ]
[ "M0010" ]
N. J. A. Sloane
2022-12-26T09:49:46
oeisdata/seq/A003/A003196.seq
aee5b1650844d0a6341bbd588caab90e
A003197
Cluster series for bond percolation problem on hexagonal lattice.
[ "1", "10", "46", "186", "706", "2568", "9004", "30894", "103832", "343006", "1123770", "3623234", "11630150" ]
[ "nonn", "more" ]
23
0
2
[ "A003197", "A003198", "A003199", "A003202" ]
[ "M4705" ]
N. J. A. Sloane
2024-11-14T23:49:59
oeisdata/seq/A003/A003197.seq
8bbd071814cd5a0cf505c186a535dc1c
A003198
Cluster series for bond percolation problem on square lattice.
[ "1", "6", "18", "48", "126", "300", "762", "1668", "4216", "8668", "21988", "43058", "110832", "202432", "561020", "875382", "2881286", "3501056" ]
[ "nonn", "more" ]
21
0
2
[ "A003197", "A003198", "A003199", "A003203", "A003207" ]
[ "M4118" ]
N. J. A. Sloane
2024-11-14T23:49:41
oeisdata/seq/A003/A003198.seq
e25d99f209994ceec6f1f9c78a4762bf
A003199
Cluster series for bond percolation problem on honeycomb.
[ "1", "4", "8", "16", "32", "54", "100", "182", "328", "494", "984", "1572", "2656", "4212", "8162", "11176", "21704", "30994", "60548" ]
[ "nonn", "more" ]
17
0
2
[ "A003197", "A003198", "A003199", "A003204" ]
[ "M3331" ]
N. J. A. Sloane
2022-02-02T23:56:56
oeisdata/seq/A003/A003199.seq
e1b36e247084e060e68b84109d401ca2
A003200
Cluster series for site percolation problem on honeycomb matching lattice (honeycomb structure with 1st, 2nd and 3rd neighbors connected).
[ "1", "12", "66", "312", "1368", "5685", "23034", "90288", "350124" ]
[ "nonn", "more" ]
20
0
2
[ "A003197", "A003198", "A003199", "A003200", "A003201", "A003202", "A003203", "A003204", "A003205", "A003206", "A003207", "A003208", "A003209", "A003210", "A003211", "A003212", "A036392", "A036394", "A036395", "A036396", "A036397", "A036398", "A036400", "A036401", "A036402" ]
[ "M4848" ]
N. J. A. Sloane
2023-04-13T11:42:31
oeisdata/seq/A003/A003200.seq
694571053c6e657f92fcf288c7fa280e