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1999-12-11 03:00:00
2025-04-28 00:58:08
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32
32
A005901
Number of points on surface of cuboctahedron (or icosahedron): a(0) = 1; for n > 0, a(n) = 10n^2 + 2. Also coordination sequence for f.c.c. or A_3 or D_3 lattice.
[ "1", "12", "42", "92", "162", "252", "362", "492", "642", "812", "1002", "1212", "1442", "1692", "1962", "2252", "2562", "2892", "3242", "3612", "4002", "4412", "4842", "5292", "5762", "6252", "6762", "7292", "7842", "8412", "9002", "9612", "10242", "10892", "11562", "12252", "12962", "13692", "14442", "15212", "16002" ]
[ "nonn", "easy", "nice" ]
111
0
2
[ "A000217", "A000290", "A001845", "A004015", "A005893", "A005894", "A005897", "A005898", "A005899", "A005901", "A005902", "A007202", "A007899", "A008137", "A010001", "A027599", "A033583", "A062786", "A063489", "A092277", "A206399", "A299254", "A299255", "A299256", "A299257", "A299258", "A299259", "A299260", "A299261", "A299262", "A299263", "A299264", "A299265", "A299266", "A299267", "A299268", "A299269", "A299272", "A299273", "A299274", "A299275", "A299276", "A299277", "A299278", "A299279", "A299280", "A299281", "A299282", "A299283", "A299284", "A299285", "A299286", "A299287", "A299288", "A299289", "A299290", "A299291", "A299292" ]
[ "M4834" ]
N. J. A. Sloane, R. Vaughan
2024-04-27T14:39:32
oeisdata/seq/A005/A005901.seq
932f07f31d7e81cc25b3f9db63e14b78
A005902
Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice.
[ "1", "13", "55", "147", "309", "561", "923", "1415", "2057", "2869", "3871", "5083", "6525", "8217", "10179", "12431", "14993", "17885", "21127", "24739", "28741", "33153", "37995", "43287", "49049", "55301", "62063", "69355", "77197", "85609", "94611", "104223", "114465", "125357", "136919", "149171", "162133", "175825", "190267", "205479" ]
[ "nonn", "easy", "nice" ]
105
0
2
[ "A001845", "A005893", "A005894", "A005897", "A005898", "A005899", "A005901", "A005902", "A005917", "A007202", "A007899", "A008137", "A010001", "A049480", "A051673", "A057813", "A063488", "A063489", "A063490", "A063491", "A063492", "A063493", "A063494", "A063495", "A063496", "A100171", "A100174", "A299254", "A299255", "A299256", "A299257", "A299258", "A299259", "A299260", "A299261", "A299262", "A299263", "A299264", "A299265", "A299266", "A299267", "A299268", "A299269", "A299272", "A299273", "A299274", "A299275", "A299276", "A299277", "A299278", "A299279", "A299280", "A299281", "A299282", "A299283", "A299284", "A299285", "A299286", "A299287", "A299288", "A299289", "A299290", "A299291", "A299292" ]
[ "M4898" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A005/A005902.seq
469b855514caba0e1cc58565b69823c9
A005903
Number of points on surface of dodecahedron: 30n^2 + 2 for n > 0.
[ "1", "32", "122", "272", "482", "752", "1082", "1472", "1922", "2432", "3002", "3632", "4322", "5072", "5882", "6752", "7682", "8672", "9722", "10832", "12002", "13232", "14522", "15872", "17282", "18752", "20282", "21872", "23522", "25232", "27002", "28832", "30722", "32672", "34682", "36752", "38882", "41072", "43322", "45632", "48002" ]
[ "nonn", "easy" ]
42
0
2
[ "A005903", "A206399" ]
[ "M5230" ]
N. J. A. Sloane.
2024-04-27T15:03:23
oeisdata/seq/A005/A005903.seq
f518f7e4d80ec49f76564f17b0b31fbf
A005904
Centered dodecahedral numbers.
[ "1", "33", "155", "427", "909", "1661", "2743", "4215", "6137", "8569", "11571", "15203", "19525", "24597", "30479", "37231", "44913", "53585", "63307", "74139", "86141", "99373", "113895", "129767", "147049", "165801", "186083", "207955", "231477", "256709", "283711", "312543", "343265", "375937", "410619", "447371", "486253", "527325" ]
[ "nonn", "easy" ]
32
0
2
[ "A001620", "A005904", "A006566" ]
[ "M5239" ]
N. J. A. Sloane.
2022-09-12T04:51:58
oeisdata/seq/A005/A005904.seq
cbf12e368b27ba34493b63be3e1179b2
A005905
Number of points on surface of truncated tetrahedron: a(n) = 14*n^2 + 2 for n > 0, a(0)=1.
[ "1", "16", "58", "128", "226", "352", "506", "688", "898", "1136", "1402", "1696", "2018", "2368", "2746", "3152", "3586", "4048", "4538", "5056", "5602", "6176", "6778", "7408", "8066", "8752", "9466", "10208", "10978", "11776", "12602", "13456", "14338", "15248", "16186", "17152", "18146", "19168", "20218", "21296", "22402", "23536", "24698" ]
[ "nonn", "easy" ]
42
0
2
[ "A005905", "A118277", "A206399" ]
[ "M5001" ]
N. J. A. Sloane
2024-11-29T17:40:39
oeisdata/seq/A005/A005905.seq
d41ebc7553f1ad033f9ffb1baa9d78c9
A005906
Truncated tetrahedral numbers: a(n) = (1/6)*(n+1)*(23*n^2 + 19*n + 6).
[ "1", "16", "68", "180", "375", "676", "1106", "1688", "2445", "3400", "4576", "5996", "7683", "9660", "11950", "14576", "17561", "20928", "24700", "28900", "33551", "38676", "44298", "50440", "57125", "64376", "72216", "80668", "89755", "99500", "109926", "121056", "132913", "145520", "158900", "173076" ]
[ "nonn", "easy" ]
74
0
2
[ "A000292", "A005906" ]
[ "M5002" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005906.seq
d6d0cc0211470390fbe86621ca319a6a
A005907
a(n) = floor(tau*a(n-2)) + a(n-1) with a(0)=1 and a(1)=3.
[ "1", "3", "4", "8", "14", "26", "48", "90", "167", "312", "582", "1086", "2027", "3784", "7063", "13185", "24613", "45946", "85770", "160112", "298890", "557956", "1041570", "1944361", "3629656", "6775698", "12648604", "23611913", "44077784", "82282661", "153602013" ]
[ "nonn" ]
12
0
2
null
null
N. J. A. Sloane
2025-01-12T14:13:21
oeisdata/seq/A005/A005907.seq
60f1953f58bbb1689c4ad527297f1228
A005908
a(n) = floor( phi*a(n-1) ) + floor( phi*a(n-2) ), where phi is the golden ratio.
[ "0", "1", "1", "2", "4", "9", "20", "46", "106", "245", "567", "1313", "3041", "7044", "16317", "37798", "87559", "202831", "469860", "1088436", "2521375", "5840796", "13530276", "31343052", "72606569", "168194019", "389623535", "902567761", "2090809436", "4843386045" ]
[ "nonn" ]
27
0
4
[ "A001622", "A005908" ]
null
N. J. A. Sloane
2022-01-15T09:51:12
oeisdata/seq/A005/A005908.seq
3235c0497e2d914f05b03b74058299ff
A005909
a(n) = floor(tau*a(n-1)) + floor(tau*a(n-2)) with a(0)=0 and a(1)=2.
[ "0", "2", "3", "7", "15", "35", "80", "185", "428", "991", "2295", "5316", "12314", "28525", "66078", "153070", "354588", "821407", "1902799", "4407857", "10210855", "23653572", "54793793", "126930502", "294036085", "681138245", "1577865210", "3655144370", "8467187363", "19614344766", "45436873440", "105255082066" ]
[ "nonn" ]
13
0
2
null
null
N. J. A. Sloane
2025-01-12T14:56:22
oeisdata/seq/A005/A005909.seq
7f7e0f2c62651a912986f388175e6c57
A005910
Truncated octahedral numbers: 16*n^3 - 33*n^2 + 24*n - 6.
[ "1", "38", "201", "586", "1289", "2406", "4033", "6266", "9201", "12934", "17561", "23178", "29881", "37766", "46929", "57466", "69473", "83046", "98281", "115274", "134121", "154918", "177761", "202746", "229969", "259526", "291513", "326026", "363161", "403014", "445681", "491258" ]
[ "nonn", "easy" ]
56
1
2
null
[ "M5266" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005910.seq
e09bc5350e21c84b2be5cbb346be46d9
A005911
Number of points on surface of truncated cube: 46n^2 + 2 for n>0.
[ "1", "48", "186", "416", "738", "1152", "1658", "2256", "2946", "3728", "4602", "5568", "6626", "7776", "9018", "10352", "11778", "13296", "14906", "16608", "18402", "20288", "22266", "24336", "26498", "28752", "31098", "33536", "36066", "38688", "41402", "44208", "47106", "50096", "53178", "56352", "59618", "62976", "66426", "69968" ]
[ "nonn", "easy" ]
28
0
2
null
[ "M5292" ]
N. J. A. Sloane.
2024-05-07T04:18:59
oeisdata/seq/A005/A005911.seq
c9a6862500d27f41941f06c3f83e8ca2
A005912
Truncated cube numbers.
[ "1", "56", "311", "920", "2037", "3816", "6411", "9976", "14665", "20632", "28031", "37016", "47741", "60360", "75027", "91896", "111121", "132856", "157255", "184472", "214661", "247976", "284571", "324600", "368217", "415576", "466831", "522136", "581645", "645512", "713891", "786936", "864801", "947640", "1035607", "1128856" ]
[ "nonn", "easy", "nice" ]
41
0
2
null
[ "M5312" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A005/A005912.seq
28cc73912cf09b0281f3d972a56db35b
A005913
a(n) = floor(tau*a(n-1)) + floor(tau*a(n-2)) with a(0)=1 and a(1)=3.
[ "1", "3", "5", "12", "27", "62", "143", "331", "766", "1774", "4109", "9518", "22048", "51074", "118313", "274073", "634893", "1470737", "3406980", "7892311", "18282636", "42351953", "98108825", "227270312", "526474502", "1219584727", "2825183178", "6544571946", "15160582256", "35119677229", "81355168809", "188460259723" ]
[ "nonn" ]
13
0
2
null
null
N. J. A. Sloane
2025-01-12T14:56:42
oeisdata/seq/A005/A005913.seq
b998caa4ec5234b2ca9c08e0cbe0064c
A005914
Number of points on surface of hexagonal prism: 12*n^2 + 2 for n > 0 (coordination sequence for W(2)).
[ "1", "14", "50", "110", "194", "302", "434", "590", "770", "974", "1202", "1454", "1730", "2030", "2354", "2702", "3074", "3470", "3890", "4334", "4802", "5294", "5810", "6350", "6914", "7502", "8114", "8750", "9410", "10094", "10802", "11534", "12290", "13070", "13874", "14702", "15554", "16430", "17330", "18254", "19202", "20174", "21170" ]
[ "nonn", "easy", "nice" ]
93
0
2
[ "A000408", "A001082", "A003154", "A005914", "A005917", "A005918", "A206399" ]
[ "M4931" ]
N. J. A. Sloane and Ralf W. Grosse-Kunstleve
2022-01-27T03:08:27
oeisdata/seq/A005/A005914.seq
26f6ab67eea3f4a8327f3ee57113f6da
A005915
Hexagonal prism numbers: a(n) = (n + 1)*(3*n^2 + 3*n + 1).
[ "1", "14", "57", "148", "305", "546", "889", "1352", "1953", "2710", "3641", "4764", "6097", "7658", "9465", "11536", "13889", "16542", "19513", "22820", "26481", "30514", "34937", "39768", "45025", "50726", "56889", "63532", "70673", "78330", "86521", "95264", "104577", "114478", "124985", "136116", "147889" ]
[ "nonn", "easy", "nice" ]
60
0
2
[ "A005915", "A143804", "A260260" ]
[ "M4933" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A005/A005915.seq
9c3f90afed510c8c6124ccf542a1940d
A005916
Molien series for a certain group of order 52.
[ "1", "0", "1", "0", "2", "1", "3", "2", "5", "4", "7", "7", "11", "11", "15", "16", "21", "22", "28", "30", "37", "39", "47", "50", "60", "63", "74", "78", "91", "95", "109", "115", "131", "137", "154", "162", "181", "190", "210", "221", "243", "255", "278", "292", "318", "333", "360", "377", "407", "425", "457", "477", "512", "533", "570", "593", "633", "658", "700", "727" ]
[ "nonn" ]
38
0
5
null
null
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A005/A005916.seq
7bbb1bd22fa214f67b532a8c4332a673
A005917
Rhombic dodecahedral numbers: a(n) = n^4 - (n - 1)^4.
[ "1", "15", "65", "175", "369", "671", "1105", "1695", "2465", "3439", "4641", "6095", "7825", "9855", "12209", "14911", "17985", "21455", "25345", "29679", "34481", "39775", "45585", "51935", "58849", "66351", "74465", "83215", "92625", "102719", "113521", "125055", "137345", "150415", "164289", "178991" ]
[ "nonn", "easy", "nice" ]
215
1
2
[ "A000290", "A000292", "A000332", "A000583", "A001844", "A001845", "A002817", "A005408", "A005894", "A005898", "A005902", "A005917", "A007588", "A008292", "A016754", "A031215", "A047969", "A049480", "A057813", "A063488", "A063489", "A063490", "A063491", "A063492", "A063493", "A063494", "A063495", "A063496", "A128195", "A176271", "A176850", "A212133", "A342354", "A344330", "A344332" ]
[ "M4968" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005917.seq
afa61386438685a7e3c1b38b41bcc58c
A005918
Number of points on surface of square pyramid: 3*n^2 + 2 (n>0).
[ "1", "5", "14", "29", "50", "77", "110", "149", "194", "245", "302", "365", "434", "509", "590", "677", "770", "869", "974", "1085", "1202", "1325", "1454", "1589", "1730", "1877", "2030", "2189", "2354", "2525", "2702", "2885", "3074", "3269", "3470", "3677", "3890", "4109", "4334", "4565", "4802", "5045", "5294", "5549", "5810", "6077", "6350", "6629" ]
[ "nonn", "easy" ]
102
0
2
[ "A005918", "A063488", "A120328", "A206399" ]
[ "M3843" ]
N. J. A. Sloane
2022-09-14T02:00:51
oeisdata/seq/A005/A005918.seq
10e6c4bd74d160123b8fabb240d5079b
A005919
Number of points on surface of tricapped prism: a(n) = 7*n^2 + 2 for n > 0, a(0)=1.
[ "1", "9", "30", "65", "114", "177", "254", "345", "450", "569", "702", "849", "1010", "1185", "1374", "1577", "1794", "2025", "2270", "2529", "2802", "3089", "3390", "3705", "4034", "4377", "4734", "5105", "5490", "5889", "6302", "6729", "7170", "7625", "8094", "8577", "9074", "9585", "10110", "10649", "11202", "11769", "12350", "12945", "13554" ]
[ "nonn", "easy" ]
35
0
2
[ "A005919", "A206399" ]
[ "M4607" ]
N. J. A. Sloane
2024-11-29T18:02:58
oeisdata/seq/A005/A005919.seq
6228d7bf6f3d9ccee65850fbf1b533bc
A005920
Tricapped prism numbers.
[ "1", "9", "33", "82", "165", "291", "469", "708", "1017", "1405", "1881", "2454", "3133", "3927", "4845", "5896", "7089", "8433", "9937", "11610", "13461", "15499", "17733", "20172", "22825", "25701", "28809", "32158", "35757", "39615", "43741", "48144", "52833", "57817", "63105", "68706", "74629", "80883", "87477", "94420" ]
[ "nonn", "easy", "nice" ]
57
0
2
[ "A000217", "A000326", "A001477", "A005920", "A005945", "A006003", "A081436", "A093445", "A125860" ]
[ "M4611" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A005/A005920.seq
706750686d47549c39b04a64c543c117
A005921
From solution to a difference equation.
[ "1", "3", "10", "48", "312", "2520", "24480", "277200", "3588480", "52254720", "845510400", "15048633600", "292190976000", "6146069529600", "139223731046400", "3379030566912000", "87478184521728000", "2406225451069440000", "70080382582898688000" ]
[ "nonn", "easy" ]
30
0
2
[ "A000045", "A000142", "A005921" ]
[ "M2871" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A005/A005921.seq
2a927d5e0cc2c79c6e8058e45b1230fc
A005922
a(1)=1; a(n) = n!*Fibonacci(n+2), n > 1.
[ "1", "6", "30", "192", "1560", "15120", "171360", "2217600", "32296320", "522547200", "9300614400", "180583603200", "3798482688000", "86044973414400", "2088355965696000", "54064489070592000", "1487129136869376000", "43312058119249920000" ]
[ "nonn", "easy" ]
27
1
2
[ "A005921", "A005922", "A078700" ]
[ "M4207" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A005/A005922.seq
6d9ec1a1d974a1b2373b7529fea4b926
A005923
From solution to a difference equation.
[ "1", "3", "13", "81", "673", "6993", "87193", "1268361", "21086113", "394368993", "8195330473", "187336699641", "4671623344753", "126204511859793", "3671695236949753", "114451527759954921", "3805443567253430593", "134436722612325267393", "5028681509898733705033", "198550708258762398282201" ]
[ "nonn", "easy" ]
49
0
2
[ "A000556", "A000557", "A005923" ]
[ "M2953" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A005/A005923.seq
3cba3357862c32f2531322080f7d7e58
A005924
From solution to a difference equation.
[ "1", "7", "49", "415", "4321", "53887", "783889", "13031935" ]
[ "nonn", "more" ]
18
1
2
null
[ "M4432" ]
N. J. A. Sloane.
2025-01-05T19:51:33
oeisdata/seq/A005/A005924.seq
e01130aabe72a8b70c42a6b90fe2c327
A005925
Theta series of diamond.
[ "1", "0", "0", "4", "0", "0", "0", "0", "12", "0", "0", "12", "0", "0", "0", "0", "6", "0", "0", "12", "0", "0", "0", "0", "24", "0", "0", "16", "0", "0", "0", "0", "12", "0", "0", "24", "0", "0", "0", "0", "24", "0", "0", "12", "0", "0", "0", "0", "8", "0", "0", "24", "0", "0", "0", "0", "48", "0", "0", "36", "0", "0", "0", "0", "6", "0", "0", "12" ]
[ "nonn", "nice" ]
28
0
4
[ "A005925", "A005926", "A005927", "A047470", "A217512", "A217513", "A217514" ]
[ "M3184" ]
N. J. A. Sloane
2021-12-18T20:41:29
oeisdata/seq/A005/A005925.seq
a6ed4327a70ba4aaf620425142fea0ab
A005926
Theta series of diamond with respect to midpoint of edge.
[ "0", "0", "0", "2", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "6", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "12", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "12", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "6", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "18", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "18", "0", "0", "0" ]
[ "easy", "nonn" ]
34
0
4
[ "A005926", "A045840", "A217513" ]
[ "M0005" ]
N. J. A. Sloane
2023-05-17T11:29:58
oeisdata/seq/A005/A005926.seq
20d37c0832c543844da90e4336fb17e2
A005927
Theta series of diamond with respect to deep hole.
[ "0", "0", "0", "4", "6", "0", "0", "0", "0", "0", "0", "12", "8", "0", "0", "0", "0", "0", "0", "12", "24", "0", "0", "0", "0", "0", "0", "16", "0", "0", "0", "0", "0", "0", "0", "24", "30", "0", "0", "0", "0", "0", "0", "12", "24", "0", "0", "0", "0", "0", "0", "24", "24", "0", "0", "0", "0", "0", "0", "36", "0", "0", "0", "0", "0", "0", "0", "12", "48", "0", "0", "0", "0", "0", "0", "28", "24", "0", "0", "0", "0", "0", "0", "36", "48", "0", "0", "0", "0", "0", "0", "24", "0", "0", "0", "0", "0" ]
[ "nonn" ]
22
0
4
null
[ "M3262" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005927.seq
b7035f7d6efd0c53127fa62fafe73c90
A005928
G.f.: s(1)^3/s(3), where s(k) = eta(q^k) and eta(q) is Dedekind's function, cf. A010815.
[ "1", "-3", "0", "6", "-3", "0", "0", "-6", "0", "6", "0", "0", "6", "-6", "0", "0", "-3", "0", "0", "-6", "0", "12", "0", "0", "0", "-3", "0", "6", "-6", "0", "0", "-6", "0", "0", "0", "0", "6", "-6", "0", "12", "0", "0", "0", "-6", "0", "0", "0", "0", "6", "-9", "0", "0", "-6", "0", "0", "0", "0", "12", "0", "0", "0", "-6", "0", "12", "-3", "0", "0", "-6", "0", "0", "0", "0", "0", "-6", "0", "6", "-6", "0", "0", "-6", "0", "6", "0", "0", "12", "0", "0", "0", "0", "0", "0", "-12", "0", "12", "0", "0", "0", "-6", "0", "0" ]
[ "sign" ]
77
0
2
[ "A005882", "A005928", "A033762", "A097195", "A113062", "A123477", "A123530", "A246838", "A253243" ]
[ "M2202" ]
N. J. A. Sloane
2024-11-14T23:49:18
oeisdata/seq/A005/A005928.seq
e1e76a7089af15be5c6a4177199b8252
A005929
Theta series of hexagonal net with respect to midpoint of edge.
[ "0", "2", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "2", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "6", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "0", "8", "0", "0", "0", "0", "0", "4", "0", "0", "0", "0", "0", "4", "0" ]
[ "easy", "nonn" ]
13
0
2
null
[ "M0006" ]
N. J. A. Sloane
2017-07-25T01:27:59
oeisdata/seq/A005/A005929.seq
6a00247c66f26994ab2397f08f6aa399
A005930
Theta series of D_5 lattice.
[ "1", "40", "90", "240", "200", "560", "400", "800", "730", "1240", "752", "1840", "1200", "2000", "1600", "2720", "1480", "3680", "2250", "3280", "2800", "4320", "2800", "5920", "2960", "5240", "3760", "6720", "4000", "7920", "4800", "6720", "5850", "8960", "4320", "10720", "6200", "9840", "7600", "11040", "5872", "12960", "7520", "12400" ]
[ "nonn", "easy" ]
31
0
2
[ "A000132", "A005930", "A008422" ]
[ "M5270" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005930.seq
021464856a7333f26a807bd3efbb716a
A005931
Theta series of the coset of the E_7 lattice in its dual.
[ "56", "576", "1512", "4032", "5544", "12096", "13664", "24192", "27216", "44352", "41832", "72576", "67536", "100800", "101304", "145728", "126504", "205632", "176456", "249984", "234360", "326592", "277200", "423360", "355320", "479808", "439992", "608832", "494928", "749952", "599760", "806400", "745416" ]
[ "nonn" ]
21
0
1
null
[ "M5313" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005931.seq
7571615e538f511414dca74f242fd3c9
A005932
Erroneous version of A003781.
[ "1", "0", "0", "56", "14", "0", "0", "576", "84", "0", "0", "1512", "280", "0", "0", "4032", "574", "0", "0", "5544", "840", "0", "0" ]
[ "dead" ]
5
0
4
null
[ "M5311" ]
null
2010-06-01T03:00:00
oeisdata/seq/A005/A005932.seq
937b0370b384ed9f0bd8014cfa313c29
A005933
Theta series of laminated lattice LAMBDA_9.
[ "1", "0", "272", "256", "3058", "2048", "11232", "7168", "32848", "16384", "67936", "32512", "139040", "59392", "217408", "95232", "385266", "147456", "528752", "226048", "819424", "315392", "1075040", "429056", "1572192", "589824" ]
[ "nonn" ]
20
0
3
null
[ "M5430" ]
N. J. A. Sloane
2021-06-16T21:04:41
oeisdata/seq/A005/A005933.seq
b907d691ff7e1e29ef89b8ca4c3b0d65
A005934
Highly powerful numbers: numbers with record value of the product of the exponents in prime factorization (A005361).
[ "1", "4", "8", "16", "32", "64", "128", "144", "216", "288", "432", "864", "1296", "1728", "2592", "3456", "5184", "7776", "10368", "15552", "20736", "31104", "41472", "62208", "86400", "108000", "129600", "194400", "216000", "259200", "324000", "432000", "518400", "648000", "972000", "1296000", "1944000", "2592000" ]
[ "nonn", "nice", "easy" ]
49
1
2
[ "A001694", "A003321", "A005188", "A005361", "A005934", "A007532", "A014576", "A023052", "A036965", "A046074", "A085629" ]
[ "M3333" ]
N. J. A. Sloane
2023-09-23T13:48:08
oeisdata/seq/A005/A005934.seq
26e459a3b18e31f458795a7b889fd551
A005935
Pseudoprimes to base 3.
[ "91", "121", "286", "671", "703", "949", "1105", "1541", "1729", "1891", "2465", "2665", "2701", "2821", "3281", "3367", "3751", "4961", "5551", "6601", "7381", "8401", "8911", "10585", "11011", "12403", "14383", "15203", "15457", "15841", "16471", "16531", "18721", "19345", "23521", "24046", "24661", "24727", "28009", "29161" ]
[ "nonn" ]
87
1
1
[ "A001567", "A005382", "A005935", "A005936", "A005937", "A005938", "A005939", "A122780" ]
[ "M5362" ]
N. J. A. Sloane.
2025-03-12T07:39:13
oeisdata/seq/A005/A005935.seq
0abebd2267b699c273d94e3e7f212260
A005936
Pseudoprimes to base 5.
[ "4", "124", "217", "561", "781", "1541", "1729", "1891", "2821", "4123", "5461", "5611", "5662", "5731", "6601", "7449", "7813", "8029", "8911", "9881", "11041", "11476", "12801", "13021", "13333", "13981", "14981", "15751", "15841", "16297", "17767", "21361", "22791", "23653", "24211", "25327", "25351", "29341", "29539" ]
[ "nonn" ]
47
1
1
[ "A001567", "A005382", "A005935", "A005936", "A005937", "A005938", "A005939", "A122782" ]
[ "M3712" ]
N. J. A. Sloane.
2025-02-16T08:32:29
oeisdata/seq/A005/A005936.seq
4a1136c93636c64417cc0c12e4b4af68
A005937
Pseudoprimes to base 6.
[ "35", "185", "217", "301", "481", "1105", "1111", "1261", "1333", "1729", "2465", "2701", "2821", "3421", "3565", "3589", "3913", "4123", "4495", "5713", "6533", "6601", "8029", "8365", "8911", "9331", "9881", "10585", "10621", "11041", "11137", "12209", "14315", "14701", "15841", "16589", "17329", "18361", "18721", "20017", "21049", "22049" ]
[ "nonn", "changed" ]
42
1
1
[ "A001567", "A005937", "A122783" ]
[ "M5246" ]
N. J. A. Sloane
2025-04-17T08:10:02
oeisdata/seq/A005/A005937.seq
1519c663718e8b7bd4a36c0edea7978d
A005938
Pseudoprimes to base 7.
[ "6", "25", "325", "561", "703", "817", "1105", "1825", "2101", "2353", "2465", "3277", "4525", "4825", "6697", "8321", "10225", "10585", "10621", "11041", "11521", "12025", "13665", "14089", "16725", "16806", "18721", "19345", "20197", "20417", "20425", "22945", "25829", "26419", "29234", "29341", "29857", "29891", "30025", "30811", "33227" ]
[ "nonn" ]
44
1
1
[ "A001567", "A005382", "A005935", "A005936", "A005937", "A005938", "A005939", "A122784" ]
[ "M4168" ]
N. J. A. Sloane.
2021-06-25T12:09:21
oeisdata/seq/A005/A005938.seq
7bec77a5afc0eb48bd5dfd9457870455
A005939
Pseudoprimes to base 10.
[ "9", "33", "91", "99", "259", "451", "481", "561", "657", "703", "909", "1233", "1729", "2409", "2821", "2981", "3333", "3367", "4141", "4187", "4521", "5461", "6533", "6541", "6601", "7107", "7471", "7777", "8149", "8401", "8911", "10001", "11111", "11169", "11649", "12403", "12801", "13833", "13981", "14701", "14817", "14911", "15211" ]
[ "nonn" ]
40
1
1
[ "A001567", "A005382", "A005939", "A121014", "A121912" ]
[ "M4612" ]
N. J. A. Sloane
2025-03-15T11:00:24
oeisdata/seq/A005/A005939.seq
3d97535a3f8e5c7a9219c6e8c1cbc2c6
A005940
The Doudna sequence: write n-1 in binary; power of prime(k) in a(n) is # of 1's that are followed by k-1 0's.
[ "1", "2", "3", "4", "5", "6", "9", "8", "7", "10", "15", "12", "25", "18", "27", "16", "11", "14", "21", "20", "35", "30", "45", "24", "49", "50", "75", "36", "125", "54", "81", "32", "13", "22", "33", "28", "55", "42", "63", "40", "77", "70", "105", "60", "175", "90", "135", "48", "121", "98", "147", "100", "245", "150", "225", "72", "343", "250", "375", "108", "625", "162", "243", "64", "17", "26", "39" ]
[ "nonn", "easy", "nice", "tabf", "look" ]
200
1
2
[ "A000040", "A000079", "A000120", "A000142", "A000265", "A001222", "A001511", "A002110", "A002450", "A003602", "A003961", "A003963", "A005940", "A005941", "A006068", "A006519", "A007814", "A007949", "A019565", "A029837", "A048793", "A053645", "A054429", "A055396", "A056239", "A059893", "A066099", "A070003", "A070826", "A070939", "A091067", "A102750", "A103969", "A106737", "A112798", "A122111", "A125106", "A156552", "A161511", "A163511", "A225546", "A241916", "A242628", "A243353", "A244154", "A246278", "A250246", "A252463", "A252464", "A252737", "A252738", "A252745", "A252750", "A252753", "A253552", "A253563", "A253565", "A253566", "A290077", "A323505", "A323508", "A323915", "A324052", "A324054", "A324055", "A324056", "A324057", "A324058", "A324106", "A324114", "A324335", "A324340", "A324348", "A324349", "A332977", "A332979", "A334866", "A337376", "A337377", "A337821", "A358134", "A358170", "A359042", "A359043" ]
[ "M0509" ]
N. J. A. Sloane and J. H. Conway
2023-03-10T16:34:28
oeisdata/seq/A005/A005940.seq
5bd06eeae7147894e6e49066ad6f45c0
A005941
Inverse of the Doudna sequence A005940.
[ "1", "2", "3", "4", "5", "6", "9", "8", "7", "10", "17", "12", "33", "18", "11", "16", "65", "14", "129", "20", "19", "34", "257", "24", "13", "66", "15", "36", "513", "22", "1025", "32", "35", "130", "21", "28", "2049", "258", "67", "40", "4097", "38", "8193", "68", "23", "514", "16385", "48", "25", "26", "131", "132", "32769", "30", "37", "72", "259", "1026", "65537", "44", "131073", "2050", "39", "64" ]
[ "nonn" ]
43
1
2
[ "A005940", "A005941", "A029747", "A103969", "A156552", "A364548", "A364549", "A364550", "A364551", "A364557", "A364558", "A364559", "A364560", "A364561", "A364562" ]
[ "M0510" ]
N. J. A. Sloane
2024-08-02T04:02:32
oeisdata/seq/A005/A005941.seq
659720591eeda998b9f8e5c54e9b3290
A005942
a(2n) = a(n) + a(n+1), a(2n+1) = 2a(n+1), if n >= 2.
[ "1", "2", "4", "6", "10", "12", "16", "20", "22", "24", "28", "32", "36", "40", "42", "44", "46", "48", "52", "56", "60", "64", "68", "72", "76", "80", "82", "84", "86", "88", "90", "92", "94", "96", "100", "104", "108", "112", "116", "120", "124", "128", "132", "136", "140", "144", "148", "152", "156", "160", "162", "164", "166", "168", "170", "172", "174", "176", "178", "180", "182" ]
[ "nonn", "easy", "nice" ]
68
0
2
[ "A005942", "A005943", "A006697", "A010060", "A275202" ]
[ "M1007" ]
N. J. A. Sloane, Jeffrey Shallit
2023-09-10T01:54:25
oeisdata/seq/A005/A005942.seq
f370637d4a9a07f2fbe9863ab35ba595
A005943
Factor complexity (number of subwords of length n) of the Golay-Rudin-Shapiro binary word A020987.
[ "1", "2", "4", "8", "16", "24", "36", "46", "56", "64", "72", "80", "88", "96", "104", "112", "120", "128", "136", "144", "152", "160", "168", "176", "184", "192", "200", "208", "216", "224", "232", "240", "248", "256", "264", "272", "280", "288", "296", "304", "312", "320", "328", "336", "344", "352", "360", "368", "376", "384", "392", "400", "408", "416", "424", "432", "440", "448", "456", "464", "472", "480", "488", "496", "504" ]
[ "nonn", "nice", "easy" ]
71
0
2
[ "A005942", "A005943", "A006697", "A337120" ]
[ "M1116" ]
N. J. A. Sloane, Jeffrey Shallit
2023-08-27T19:46:33
oeisdata/seq/A005/A005943.seq
b0d14bf2ef42325c79e82d1fb8d84094
A005944
Theta series of 18-dimensional lattice associated with Sp_4(4), with det 1024 and minimal norm 4.
[ "1", "0", "3060", "77760", "774180", "4621824", "19873920", "68181120", "198425700", "509271040", "1183095144", "2535128640", "5085536640", "9652170240", "17458087680", "30306142080", "50807986020", "82540293120", "130341238900", "200859721920" ]
[ "nonn", "easy" ]
7
0
3
[ "A005944", "A005950" ]
null
N. J. A. Sloane.
2012-03-30T16:44:53
oeisdata/seq/A005/A005944.seq
eb3dc4cf9ebc943f2bbf53127442167d
A005945
Number of n-step mappings with 4 inputs.
[ "0", "1", "15", "60", "154", "315", "561", "910", "1380", "1989", "2755", "3696", "4830", "6175", "7749", "9570", "11656", "14025", "16695", "19684", "23010", "26691", "30745", "35190", "40044", "45325", "51051", "57240", "63910", "71079", "78765", "86986", "95760", "105105", "115039", "125580", "136746" ]
[ "nonn", "easy" ]
49
0
3
[ "A000217", "A005920", "A005945", "A006003", "A081436", "A094952", "A125860" ]
[ "M4966" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A005/A005945.seq
0b31cbb601dfeaaca7a05ccbb6a8e494
A005946
Number of n-step mappings with 5 inputs.
[ "1", "52", "358", "1304", "3455", "7556", "14532", "25488", "41709", "64660", "95986", "137512", "191243", "259364", "344240", "448416", "574617", "725748", "904894", "1115320", "1360471", "1643972", "1969628", "2341424", "2763525", "3240276", "3776202", "4376008", "5044579", "5786980", "6608456", "7514432", "8510513", "9602484" ]
[ "nonn", "easy" ]
31
1
2
[ "A005946", "A144150" ]
[ "M5303" ]
N. J. A. Sloane.
2022-05-20T04:40:28
oeisdata/seq/A005/A005946.seq
78bb3dd7cc7712577ea5e92a070f1f8d
A005947
Tumbling distance for n-input mappings with 2 steps.
[ "0", "3", "16", "75", "356", "1770", "9306", "51821", "305232", "1897227", "12411650", "85234864", "612903324", "4604004691", "36050248752", "293659886235", "2483993559376", "21781908622738", "197701336871190", "1854695911048053", "17960309481562600", "179309794875495795" ]
[ "nonn" ]
21
0
2
null
[ "M3016" ]
N. J. A. Sloane.
2018-06-15T08:45:06
oeisdata/seq/A005/A005947.seq
6bcc2a2b7cf1b025d9c40ca87476c872
A005948
Tumbling distance for n-input mappings with 3 steps.
[ "0", "6", "52", "411", "3392", "30070", "287802", "2969267", "32902560", "389989449", "4924511300", "65995764461", "935412316380", "13978234748257", "219593721606826", "3617245945896600", "62330776215811680", "1121143456571006754", "21008889235589947362" ]
[ "nonn" ]
21
0
2
null
[ "M4262" ]
N. J. A. Sloane.
2018-06-15T08:45:18
oeisdata/seq/A005/A005948.seq
bda9fce318965f0524f386534633d31f
A005949
Tumbling distance for n-input mappings with 4 steps.
[ "0", "10", "120", "1335", "15708", "200610", "2790510", "42159117", "688622328", "12101137137", "227715010610", "4568825493485", "97357110723876", "2195590326037459", "52236953438239276", "1307388516417151770", "34332703353547941888", "943774667840796564132" ]
[ "nonn" ]
21
0
2
null
[ "M4737" ]
N. J. A. Sloane.
2018-06-15T08:45:28
oeisdata/seq/A005/A005949.seq
3546bfd9a72097bd4a2de473745b10c5
A005950
Theta series of 18-dimensional lattice associated with Sp_4(4), with det 256 and minimal norm 3.
[ "1", "0", "0", "240", "3060", "19584", "77760", "249120", "774180", "2110720", "4621824", "9294480", "19873920", "40049280", "68181120", "110984160", "198425700", "342524160", "509271040", "735758640", "1183095144" ]
[ "nonn", "easy", "nice" ]
12
0
4
[ "A005944", "A005950" ]
[ "M5417" ]
N. J. A. Sloane
2021-12-18T20:40:42
oeisdata/seq/A005/A005950.seq
03fd4f08d4b7c19493d94e195aa4d42e
A005951
Theta series of P_{9a} packing.
[ "1", "0", "0", "0", "306", "0", "0", "0", "3024", "512", "0", "0", "13344", "0", "0", "0", "36594", "4608", "0", "0", "78048", "0", "0", "0", "149088", "18432", "0", "0", "256896", "0", "0", "0", "405072", "47616", "0", "0", "620306", "0", "0", "0", "900576" ]
[ "nonn" ]
9
0
5
null
[ "M5436" ]
N. J. A. Sloane.
2012-03-30T16:44:53
oeisdata/seq/A005/A005951.seq
b1f993a8a271a1c78403af451ad89bd3
A005952
Theta series of P_{12a} packing.
[ "1", "0", "840", "2560", "26376", "30720", "204960", "168960", "843528", "593920", "2625840", "1605120", "6435744", "3717120", "14118720", "7633920", "26992392", "14192640", "49806120", "24752640", "82451376" ]
[ "nonn", "more" ]
12
0
3
null
[ "M5481" ]
N. J. A. Sloane
2021-05-19T21:18:10
oeisdata/seq/A005/A005952.seq
4cb9c2fdf4d016950e4fd63e499806d0
A005953
Theta series of P_{11a} packing.
[ "1", "0", "566", "1280", "12188", "12800", "75304", "58880", "275126", "179200", "757240", "441600", "1711224", "949760", "3405696", "1799680", "6261404", "3138560", "10613550", "5216000", "16987640" ]
[ "nonn", "easy" ]
9
0
3
null
[ "M5464" ]
N. J. A. Sloane.
2012-03-30T16:44:53
oeisdata/seq/A005/A005953.seq
c3ace495b7ae86d41e8e1957e950bbbd
A005954
Theta series of P_{10b} packing.
[ "1", "500", "7220", "36800", "118580", "288424", "589760", "1104000", "1884980", "2994740", "4618024" ]
[ "nonn" ]
9
0
2
null
[ "M5456" ]
N. J. A. Sloane.
2012-03-30T16:44:53
oeisdata/seq/A005/A005954.seq
02928172bcfcba23bde5e24e595226d6
A005955
Number of acyclic secondary alcohols with n carbon atoms.
[ "1", "2", "5", "14", "36", "98", "273", "768", "2197", "6360", "18584", "54780", "162672", "486154", "1461197", "4413988", "13393855", "40807290", "124783669", "382842018", "1178140280", "3635626680", "11247841224", "34880346840", "108402132544", "337576497920", "1053229358252", "3291813720292" ]
[ "nonn" ]
15
3
2
[ "A000625", "A005955" ]
[ "M1453" ]
N. J. A. Sloane.
2016-12-26T15:20:53
oeisdata/seq/A005/A005955.seq
ae7ba1c3bfa0a854d7ec2954390b483c
A005956
Number of acyclic tertiary alcohols with n carbon atoms.
[ "1", "1", "3", "10", "27", "79", "234", "686", "2036", "6080", "18224", "54920", "166245", "505201", "1541014", "4716540", "14480699", "44586619", "137648341", "425992838", "1321362034", "4107332002", "12792440104", "39915889304", "124762916912", "390594099694", "1224682772872", "3845389399882" ]
[ "nonn" ]
14
4
3
null
[ "M2838" ]
N. J. A. Sloane.
2016-12-26T15:21:36
oeisdata/seq/A005/A005956.seq
476ea32cb088665388d369d51e88a911
A005957
Number of acyclic ketone and aldehyde stereo-isomers with n carbon atoms.
[ "1", "1", "2", "3", "8", "18", "47", "123", "338", "935", "2657", "7616", "22138", "64886", "191873", "571169", "1711189", "5153883", "15599094", "47415931", "144692886", "443091572", "1361233280", "4194107380", "12957209782", "40128629400", "124562327944", "387467513732", "1207633413980" ]
[ "nonn" ]
18
1
3
null
[ "M0880" ]
N. J. A. Sloane.
2019-07-24T19:34:25
oeisdata/seq/A005/A005957.seq
2d8b86fb199df2b2babeddeadf921fc7
A005958
Number of esters with n carbon atoms up to stereo-isomerism.
[ "1", "2", "4", "10", "25", "64", "172", "472", "1319", "3750", "10796", "31416", "92276", "273172", "814246", "2441688", "7360877", "22295746", "67819576", "207083944", "634512581", "1950301202", "6011920720", "18581123978", "57568802820", "178763375468", "556255762692", "1734248037856" ]
[ "nonn" ]
22
2
2
null
[ "M1210" ]
N. J. A. Sloane.
2025-02-01T23:20:12
oeisdata/seq/A005/A005958.seq
0dba8c10bf0e5e740856750dca6ed39b
A005959
Number of acyclic ethylene derivatives with n carbon atoms.
[ "1", "1", "4", "6", "18", "42", "118", "314", "895", "2521", "7307", "21238", "62566", "185310", "553288", "1660490", "5011299", "15190665", "46244031", "141296042", "433204573", "1332261200", "4108833222", "12704949506", "39379343929", "122327632914", "380778749899", "1187544117426" ]
[ "nonn" ]
15
2
3
null
[ "M3286" ]
N. J. A. Sloane.
2016-12-26T15:22:49
oeisdata/seq/A005/A005959.seq
2bd37e5ad6b034dd7e239d8b30135002
A005960
Number of acyclic disubstituted alkanes with n carbon atoms and distinct substituents.
[ "1", "3", "8", "23", "69", "208", "636", "1963", "6099", "19059", "59836", "188576", "596252", "1890548", "6008908", "19139155", "61074583", "195217253", "624913284", "2003090071", "6428430129", "20653101216", "66420162952", "213802390264", "688796847976", "2220789746752", "7165331870036" ]
[ "nonn" ]
34
1
2
[ "A005960", "A193418" ]
[ "M2747" ]
N. J. A. Sloane
2018-01-10T09:05:10
oeisdata/seq/A005/A005960.seq
794432dcacf2b4a38755c3e9a765097e
A005961
Number of acyclic disubstituted alkanes with n carbon atoms and identical substituents.
[ "1", "2", "5", "13", "37", "108", "325", "993", "3070", "9564", "29979", "94392", "298311", "945592", "3005021", "9570559", "30539044", "97611676", "312462096", "1001554565", "3214232129", "10326580526", "33210135104", "106901289420", "344398593149", "1110395171502", "3582666470285", "11567123373968" ]
[ "nonn" ]
26
1
2
[ "A005960", "A005961" ]
[ "M1447" ]
N. J. A. Sloane
2024-12-29T00:52:56
oeisdata/seq/A005/A005961.seq
6ba193fe5f09a552a92ada2978d58e10
A005962
Number of carbon trees with n carbon atoms.
[ "1", "1", "2", "4", "10", "22", "60", "158", "439", "1229", "3525", "10178", "29802", "87862", "261204", "781198", "2350249", "7105081", "21577415", "65787902", "201313311", "618040002", "1903102730", "5876174472", "18189503139", "56435742554", "175477142565", "546703920430", "1706433403626" ]
[ "nonn" ]
22
1
3
null
[ "M1962" ]
N. J. A. Sloane
2017-02-09T06:19:26
oeisdata/seq/A005/A005962.seq
0bb31a64ee679d31c18b0ee6cf805d8b
A005963
Number of restricted hexagonal polyominoes with n cells.
[ "0", "0", "1", "2", "10", "45", "210", "1002", "4883", "23797", "116518", "571471" ]
[ "nonn" ]
9
1
4
[ "A000228", "A001998", "A002216", "A005963", "A036359" ]
[ "M1969" ]
N. J. A. Sloane.
2012-03-30T16:44:53
oeisdata/seq/A005/A005963.seq
751b2bfaa4ffd4d21955c518022ec7f8
A005964
Number of trivalent connected (or cubic) planar graphs with 2n nodes.
[ "0", "1", "1", "3", "9", "32", "133", "681", "3893", "24809", "169206", "1214462", "9034509", "69093299", "539991437" ]
[ "nonn", "nice", "hard" ]
50
1
4
[ "A000109", "A002851", "A005964", "A058378", "A204186" ]
[ "M2816" ]
N. J. A. Sloane
2025-04-08T12:23:26
oeisdata/seq/A005/A005964.seq
7af75169e3b6124dfbe25d39afcfd9f1
A005965
Erroneous version of A000421.
[ "1", "2", "6", "20", "91", "506" ]
[ "dead" ]
16
1
2
null
[ "M1651" ]
N. J. A. Sloane
2017-10-12T04:19:17
oeisdata/seq/A005/A005965.seq
dfc6032349423b48d1694090544b318d
A005966
Number of trivalent planar loopless multigraphs with 2n nodes.
[ "1", "2", "5", "17", "71", "357", "2143", "14960", "116560", "986983", "8874072" ]
[ "nonn", "more" ]
14
1
2
[ "A000421", "A005957", "A005966" ]
[ "M1511" ]
N. J. A. Sloane.
2016-10-25T14:26:47
oeisdata/seq/A005/A005966.seq
4fd451b8246d8f72ede04405cb0a5294
A005967
Number of isomorphism classes of connected 3-regular multigraphs of order 2n, loops allowed.
[ "2", "5", "17", "71", "388", "2592", "21096", "204638", "2317172", "30024276", "437469859", "7067109598", "125184509147", "2410455693765", "50101933643655", "1117669367609605", "26629298567576331", "674793598023809924", "18119844622209998036" ]
[ "nonn" ]
45
1
1
[ "A000421", "A005967", "A085549", "A129427", "A129430", "A129432", "A129434", "A129436", "A333397" ]
[ "M1512" ]
N. J. A. Sloane
2023-11-19T01:55:07
oeisdata/seq/A005/A005967.seq
f253b8a422ce5a0bd6511beff2a4e32e
A005968
Sum of cubes of first n Fibonacci numbers.
[ "0", "1", "2", "10", "37", "162", "674", "2871", "12132", "51436", "217811", "922780", "3908764", "16558101", "70140734", "297121734", "1258626537", "5331629710", "22585142414", "95672204155", "405273951280", "1716768021816", "7272346018247", "30806152127640", "130496954475672", "552793970116297", "2341672834801754" ]
[ "nonn", "easy" ]
86
0
3
[ "A000071", "A001654", "A003628", "A005968", "A005969", "A045468", "A047650", "A056570", "A098531", "A098532", "A098533", "A119284", "A128697" ]
[ "M1967" ]
N. J. A. Sloane
2025-01-05T19:51:33
oeisdata/seq/A005/A005968.seq
92d9f939138755e5fdf1f89e0a6239ad
A005969
Sum of fourth powers of Fibonacci numbers.
[ "1", "2", "18", "99", "724", "4820", "33381", "227862", "1564198", "10714823", "73457064", "503438760", "3450734281", "23651386922", "162109796922", "1111115037483", "7615701104764", "52198777931900", "357775783071021", "2452231602371646", "16807845698458702" ]
[ "nonn", "easy" ]
49
1
2
[ "A000071", "A001654", "A005968", "A005969", "A098531", "A098532", "A098533", "A119285", "A128697" ]
[ "M2106" ]
N. J. A. Sloane
2022-09-08T08:44:34
oeisdata/seq/A005/A005969.seq
3d4c6e6454f42817d75c6d35db2fde3d
A005970
Partial sums of squares of Lucas numbers.
[ "1", "10", "26", "75", "196", "520", "1361", "3570", "9346", "24475", "64076", "167760", "439201", "1149850", "3010346", "7881195", "20633236", "54018520", "141422321", "370248450", "969323026", "2537720635", "6643838876", "17393796000", "45537549121", "119218851370" ]
[ "nonn", "easy" ]
45
1
2
[ "A000032", "A005970", "A215602" ]
[ "M4689" ]
N. J. A. Sloane
2024-07-09T09:07:17
oeisdata/seq/A005/A005970.seq
81895c43d7df933aba417058dd5f1627
A005971
Partial sums of cubes of Lucas numbers.
[ "1", "28", "92", "435", "1766", "7598", "31987", "135810", "574786", "2435653", "10316252", "43702500", "185123261", "784200368", "3321916912", "14071880655", "59609419066", "252509590018", "1069647725567", "4531100578950", "19194049901126", "81307300410353" ]
[ "nonn" ]
37
1
2
null
[ "M5198" ]
N. J. A. Sloane
2022-04-13T13:25:18
oeisdata/seq/A005/A005971.seq
7e989867b66b2c496876de4505728377
A005972
Partial sums of fourth powers of Lucas numbers.
[ "1", "82", "338", "2739", "17380", "122356", "829637", "5709318", "39071494", "267958135", "1836197336", "12586569192", "86266785673", "591288786874", "4052734152890", "27777904133691", "190392453799372", "1304969641560028", "8944394070807629" ]
[ "nonn" ]
45
1
2
null
[ "M5358" ]
N. J. A. Sloane
2022-04-13T13:25:18
oeisdata/seq/A005/A005972.seq
0a5df015cfa628d3a7cd1964751b15d3
A005973
Number of connected labeled interval graphs with n nodes.
[ "1", "1", "4", "35", "541", "13062", "444767", "19912657", "1121041222", "77048430033", "6329916102841", "611728117464928", "68657066350744197", "8854866422322096893", "1300613343254300891316" ]
[ "nonn", "nice" ]
14
1
3
null
[ "M3658" ]
N. J. A. Sloane
2021-12-18T20:40:20
oeisdata/seq/A005/A005973.seq
bd4825c05b8aae6005bd20993be2f4e8
A005974
Number of unlabeled connected identity interval graphs with n nodes.
[ "1", "0", "0", "0", "0", "4", "27", "172", "1141", "8017", "60319", "486372", "4196384", "38621356", "377949874", "3920335179", "42975606304", "496545261764", "6031989895262", "76867521958187", "1025417405366410", "14292224499308110", "207763603833695113", "3144818752057400765" ]
[ "nonn", "nice" ]
20
1
6
null
[ "M3617" ]
N. J. A. Sloane
2021-12-18T20:40:09
oeisdata/seq/A005/A005974.seq
2be68984ee9abc1bcedf9ddd4af33020
A005975
Number of interval graphs on n unlabeled nodes.
[ "1", "2", "4", "10", "27", "92", "369", "1807", "10344", "67659", "491347", "3894446", "33278992", "304256984", "2960093835", "30523315419", "332524557107", "3816805831381", "46048851321131", "582691924941142", "7717878059859874", "106806430860694984", "1541683193805924288", "23173865491070682522" ]
[ "nonn" ]
36
1
2
null
[ "M1224" ]
N. J. A. Sloane
2022-08-22T11:12:18
oeisdata/seq/A005/A005975.seq
7ede015fbda8cded015f2c83a60655e4
A005976
Number of unlabeled connected interval graphs with n nodes.
[ "1", "1", "2", "5", "15", "56", "250", "1328", "8069", "54962", "410330", "3317302", "28774874", "266242936", "2616100423", "27205605275", "298569256590", "3449309394415", "41854968275924", "532353636671777", "7083840662453415", "98443312509634266", "1426382369328881332" ]
[ "nonn", "nice" ]
18
1
3
null
[ "M1487" ]
N. J. A. Sloane
2021-12-18T20:39:53
oeisdata/seq/A005/A005976.seq
71d57bc280359405bdd913d0c0032477
A005977
Reduced interval graphs with n nodes.
[ "0", "0", "0", "0", "1", "2", "7", "31", "168", "1025", "7013", "52495", "425213", "3696032", "34291937", "338161526", "3532185118", "38963334652", "452704892533", "5526901638291", "70746674291507" ]
[ "nonn" ]
10
1
6
null
[ "M1787" ]
N. J. A. Sloane.
2018-01-10T03:15:44
oeisdata/seq/A005/A005977.seq
91a2d97e2767f67d091dd4f09aa1e191
A005978
Number of dependable interval graphs with n nodes.
[ "0", "0", "0", "0", "1", "4", "19", "93", "539", "3474", "24856", "192972", "1613219", "14410374", "136920388", "1378542639", "14663082556", "164340455701", "1936286904952", "23932267735948", "309701296575063" ]
[ "nonn" ]
10
1
6
null
[ "M3554" ]
N. J. A. Sloane.
2018-01-10T03:15:52
oeisdata/seq/A005/A005978.seq
c24c15685c151859222a05d4fca2b40a
A005979
Number of Hamiltonian rooted triangulations with n internal nodes and 5 external nodes.
[ "5", "45", "420", "4130", "42480", "453350", "4986860", "56251230", "648055650", "7601584050", "90556803600", "1093417607850", "13359234113250", "164935358510470", "2055350730457020", "25827268868350690", "326989527294142480", "4168165020885948440", "53462092704596804720" ]
[ "nonn" ]
17
0
1
null
[ "M4000" ]
N. J. A. Sloane.
2017-02-28T16:10:18
oeisdata/seq/A005/A005979.seq
7e5c5ac37b518dd4dcbd3e873d8148a1
A005980
Let F(x) = 1 + x + 4x^2 + 9x^3 + ... = g.f. for A002835 (solid partitions restricted to two planes) and expand (1-x)(1-x^2)(1-x^3)...*F(x) in powers of x.
[ "1", "0", "2", "4", "9", "16", "35", "63", "129", "234", "445", "798", "1458", "2568", "4561", "7924", "13770", "23584", "40301", "68097", "114646", "191336", "317893", "524396", "861054", "1405130", "2282651", "3688254", "5933463" ]
[ "nonn", "more" ]
13
0
3
[ "A002836", "A005980" ]
[ "M1169" ]
N. J. A. Sloane.
2017-10-12T12:38:44
oeisdata/seq/A005/A005980.seq
99ce589ff9dc6f6e3e5f6accf6103da0
A005981
Number of 2 up, 2 down, 2 up, ... permutations of length 2n + 1.
[ "1", "1", "6", "71", "1456", "45541", "2020656", "120686411", "9336345856", "908138776681", "108480272749056", "15611712012050351", "2664103110372192256", "531909061958526321421", "122840808510269863827456", "32491881630252866646683891", "9758611490955498257378246656" ]
[ "nonn" ]
48
0
3
[ "A005981", "A058258", "A076417", "A131453", "A131454", "A131455" ]
[ "M4276" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005981.seq
c4e9a5cbc09a1e6c8f7cea5e74458c56
A005982
3 up, 3 down, 3 up, ... permutations of length 3n+1.
[ "1", "20", "1301", "202840", "61889101", "32676403052", "27418828825961", "34361404413755056", "61335081309931829401", "150221740688275657957940", "489799709605132718770274141", "2073641570051429601078643837960", "11163099186064084100687107863253381" ]
[ "nonn" ]
20
1
2
[ "A005982", "A229884" ]
[ "M5107" ]
N. J. A. Sloane.
2017-10-16T01:57:47
oeisdata/seq/A005/A005982.seq
050c45bb894b1667d1e60f9e0b94736a
A005983
Number of 4 up, 4 down, 4 up, ... permutations of length 4n+1.
[ "1", "1", "70", "26599", "33757360", "107709888805", "726401013530416", "9197888739246870571", "200656681438694771057920", "7065183006232334215872360169", "381446884048286939903298793116160", "30299510478473850351087119774475282895", "3422529682416045761005260546463028151218176" ]
[ "nonn" ]
25
0
3
[ "A005983", "A229885" ]
[ "M5347" ]
N. J. A. Sloane.
2017-10-16T14:47:00
oeisdata/seq/A005/A005983.seq
d4fc6bac827129b43fcfd1ef2439e621
A005984
Related to recurrences over rings.
[ "1", "2", "5", "6", "10", "14", "21", "22", "27", "32", "42", "48", "59", "70", "85" ]
[ "nonn", "more" ]
46
1
2
[ "A005984", "A093005" ]
[ "M1323" ]
N. J. A. Sloane
2022-10-17T01:45:51
oeisdata/seq/A005/A005984.seq
53c48c84cec4ef8e103d07c66294e880
A005985
Length of longest trail (i.e., path with all distinct edges) on the edges of an n-cube.
[ "0", "1", "4", "9", "32", "65", "192", "385", "1024", "2049", "5120", "10241", "24576", "49153", "114688", "229377", "524288", "1048577", "2359296", "4718593", "10485760", "20971521", "46137344", "92274689", "201326592", "402653185", "872415232", "1744830465", "3758096384", "7516192769", "16106127360", "32212254721" ]
[ "nonn", "nice", "easy" ]
49
0
3
[ "A005985", "A018215" ]
[ "M3366" ]
Colin Mallows
2022-09-08T08:44:34
oeisdata/seq/A005/A005985.seq
15f37298ca054b3484fc59b0bdfd014c
A005986
Number of column-strict plane partitions of n.
[ "1", "2", "5", "11", "23", "45", "87", "160", "290", "512", "889", "1514", "2547", "4218", "6909", "11184", "17926", "28449", "44772", "69862", "108205", "166371", "254107", "385617", "581729", "872535", "1301722", "1932006", "2853530", "4194867", "6139361", "8946742", "12984724", "18771092", "27033892" ]
[ "nonn" ]
47
0
2
[ "A003293", "A005986" ]
[ "M1393" ]
N. J. A. Sloane
2018-09-27T12:30:57
oeisdata/seq/A005/A005986.seq
0aee35eab142d755ad1a6911d73c8ee1
A005987
Number of symmetric plane partitions of n.
[ "1", "1", "1", "2", "3", "4", "6", "8", "12", "16", "22", "29", "41", "53", "71", "93", "125", "160", "211", "270", "354", "450", "581", "735", "948", "1191", "1517", "1902", "2414", "3008", "3791", "4709", "5909", "7311", "9119", "11246", "13981", "17178", "21249", "26039", "32105", "39213", "48159", "58669", "71831", "87269" ]
[ "nonn", "nice", "easy" ]
45
0
4
[ "A000219", "A000784", "A000785", "A000786", "A005987", "A048142" ]
[ "M0562" ]
N. J. A. Sloane
2018-09-27T12:32:08
oeisdata/seq/A005/A005987.seq
851c2da9437c55c0a253277f03a1ed38
A005988
x^3 + n*y^3 = 1 is solvable.
[ "2", "7", "9", "17", "19", "20", "26", "28", "37", "43", "63", "65", "91", "124", "126", "182", "215", "217", "254", "342", "344", "422", "511", "513", "614", "635", "651", "728", "730", "813", "999", "1001", "1330", "1332", "1521", "1588", "1657", "1727", "1729", "1801", "1876", "1953", "2196", "2198", "2743", "2745", "3155", "3374", "3376" ]
[ "nonn" ]
31
1
1
[ "A005988", "A055735", "A259453" ]
[ "M1732" ]
N. J. A. Sloane
2018-10-04T02:14:58
oeisdata/seq/A005/A005988.seq
90a011c627b5b6725a467b002fc57d7d
A005989
Values B(2,n)/4 of Gandhi polynomials defined by B(x,0)=x and B(x,n) = x^2 (B(x+1,n-1) - B(x,n-1)).
[ "1", "5", "43", "557", "10075", "241949", "7437547", "284618381", "13263233659", "739273581053", "48558705881611", "3711738956813165", "326635178650696603", "32785012192388829917", "3722823724366317825835", "474819247115650709778509" ]
[ "nonn", "easy" ]
14
0
2
null
[ "M3998" ]
N. J. A. Sloane.
2022-10-30T18:19:58
oeisdata/seq/A005/A005989.seq
8ae29345522891c4c4a5f8fe5c1bb48d
A005990
a(n) = (n-1)*(n+1)!/6.
[ "0", "1", "8", "60", "480", "4200", "40320", "423360", "4838400", "59875200", "798336000", "11416204800", "174356582400", "2833294464000", "48819843072000", "889218570240000", "17072996548608000", "344661117825024000", "7298706024529920000", "161787983543746560000" ]
[ "nonn", "easy" ]
82
1
3
[ "A001113", "A001620", "A001715", "A005990", "A090672", "A091725", "A099285", "A167568" ]
[ "M4551" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005990.seq
506a45ee491e9da70c37f7fbe7ac810d
A005991
Let k(m) denote the least integer such that every m X m (0,1)-matrix with exactly k(m) ones in each row and in each column contains a 2 X 2 submatrix without zeros. The sequence gives the index n of the last term in each string of equal entries in the {k(m)} sequence (see A155934).
[ "2", "6", "12", "20", "30", "43" ]
[ "nonn", "more" ]
21
1
1
[ "A003509", "A005991", "A155934" ]
[ "M1582" ]
N. J. A. Sloane
2024-01-10T23:56:02
oeisdata/seq/A005/A005991.seq
a641012d5bbc15b2175c20cd0b727493
A005992
Erroneous version of A011260.
[ "1", "1", "2", "2", "6", "4", "18", "16", "48", "60" ]
[ "dead" ]
6
1
3
null
[ "M0353" ]
null
2010-06-01T03:00:00
oeisdata/seq/A005/A005992.seq
a5ab92423706179e6652a9ba617f8b4b
A005993
Expansion of (1+x^2)/((1-x)^2*(1-x^2)^2).
[ "1", "2", "6", "10", "19", "28", "44", "60", "85", "110", "146", "182", "231", "280", "344", "408", "489", "570", "670", "770", "891", "1012", "1156", "1300", "1469", "1638", "1834", "2030", "2255", "2480", "2736", "2992", "3281", "3570", "3894", "4218", "4579", "4940", "5340", "5740", "6181", "6622", "7106", "7590", "8119", "8648", "9224", "9800" ]
[ "nonn", "easy", "nice" ]
148
0
2
[ "A002260", "A005408", "A005993", "A005995", "A008619", "A008794", "A018211", "A018213", "A062136", "A177878", "A254338", "A282011" ]
[ "M1576" ]
N. J. A. Sloane, Winston C. Yang (yang(AT)math.wisc.edu)
2024-09-24T14:14:31
oeisdata/seq/A005/A005993.seq
ad5a56cd758cd7256648934616447be2
A005994
Alkane (or paraffin) numbers l(7,n).
[ "1", "3", "9", "19", "38", "66", "110", "170", "255", "365", "511", "693", "924", "1204", "1548", "1956", "2445", "3015", "3685", "4455", "5346", "6358", "7514", "8814", "10283", "11921", "13755", "15785", "18040", "20520", "23256", "26248", "29529", "33099", "36993", "41211", "45790", "50730", "56070", "61810", "67991" ]
[ "nonn", "easy", "nice" ]
87
0
2
[ "A000217", "A005408", "A005993", "A005994", "A005997", "A006009", "A282011" ]
[ "M2774" ]
N. J. A. Sloane, Winston C. Yang (yang(AT)math.wisc.edu)
2025-03-08T13:27:33
oeisdata/seq/A005/A005994.seq
73fb6b214ef662c2540f011cccd66f5c
A005995
Alkane (or paraffin) numbers l(8,n).
[ "1", "3", "12", "28", "66", "126", "236", "396", "651", "1001", "1512", "2184", "3108", "4284", "5832", "7752", "10197", "13167", "16852", "21252", "26598", "32890", "40404", "49140", "59423", "71253", "85008", "100688", "118728", "139128", "162384", "188496", "218025", "250971", "287964", "329004", "374794", "425334", "481404", "543004" ]
[ "nonn", "easy" ]
66
0
2
[ "A005995", "A018210", "A053132", "A160770", "A271870" ]
[ "M2916" ]
N. J. A. Sloane, Winston C. Yang (yang(AT)math.wisc.edu)
2018-03-30T19:45:28
oeisdata/seq/A005/A005995.seq
19901a5649cafc271b86a101dda8b3cf
A005996
G.f.: 2*(1-x^3)/((1-x)^5*(1+x)^2).
[ "2", "6", "16", "30", "54", "84", "128", "180", "250", "330", "432", "546", "686", "840", "1024", "1224", "1458", "1710", "2000", "2310", "2662", "3036", "3456", "3900", "4394", "4914", "5488", "6090", "6750", "7440", "8192", "8976", "9826", "10710", "11664", "12654", "13718" ]
[ "nonn", "easy" ]
50
1
1
[ "A005996", "A034828" ]
[ "M1609" ]
N. J. A. Sloane
2025-02-16T08:32:29
oeisdata/seq/A005/A005996.seq
bcd7dcdb2acc6084b1d822902a9bbcce
A005997
Number of paraffins.
[ "1", "3", "10", "20", "39", "63", "100", "144", "205", "275", "366", "468", "595", "735", "904", "1088", "1305", "1539", "1810", "2100", "2431", "2783", "3180", "3600", "4069", "4563", "5110", "5684", "6315", "6975", "7696", "8448", "9265", "10115", "11034", "11988", "13015", "14079", "15220", "16400", "17661", "18963", "20350", "21780", "23299" ]
[ "nonn", "easy" ]
54
1
2
[ "A005997", "A005999" ]
[ "M2832" ]
N. J. A. Sloane
2024-12-29T10:38:06
oeisdata/seq/A005/A005997.seq
c23107181741f5cc1f1dc609c40f7f2c
A005998
Number of paraffins.
[ "1", "2", "7", "14", "29", "48", "79", "116", "169", "230", "311", "402", "517", "644", "799", "968", "1169", "1386", "1639", "1910", "2221", "2552", "2927", "3324", "3769", "4238", "4759", "5306", "5909", "6540", "7231", "7952", "8737", "9554", "10439", "11358", "12349", "13376", "14479", "15620", "16841", "18102", "19447", "20834", "22309" ]
[ "nonn", "easy" ]
40
1
2
null
[ "M1740" ]
N. J. A. Sloane
2024-10-13T13:37:05
oeisdata/seq/A005/A005998.seq
3c68ddb8169f148f2f361676fc6a857b
A005999
Number of paraffins.
[ "1", "2", "6", "11", "23", "38", "64", "95", "141", "194", "266", "347", "451", "566", "708", "863", "1049", "1250", "1486", "1739", "2031", "2342", "2696", "3071", "3493", "3938", "4434", "4955", "5531", "6134", "6796", "7487", "8241", "9026", "9878", "10763", "11719", "12710", "13776", "14879", "16061", "17282", "18586", "19931", "21363", "22838", "24404", "26015", "27721", "29474", "31326", "33227", "35231", "37286" ]
[ "nonn", "easy" ]
37
1
2
[ "A005997", "A005999" ]
[ "M1577" ]
N. J. A. Sloane
2023-07-14T14:23:16
oeisdata/seq/A005/A005999.seq
2753b6f29d93c1a146c12dcfd6560f24
A006000
a(n) = (n+1)*(n^2+n+2)/2; g.f.: (1 + 2*x^2) / (1 - x)^4.
[ "1", "4", "12", "28", "55", "96", "154", "232", "333", "460", "616", "804", "1027", "1288", "1590", "1936", "2329", "2772", "3268", "3820", "4431", "5104", "5842", "6648", "7525", "8476", "9504", "10612", "11803", "13080", "14446", "15904", "17457", "19108", "20860", "22716", "24679", "26752", "28938", "31240", "33661", "36204", "38872", "41668", "44595", "47656", "50854", "54192" ]
[ "nonn", "easy" ]
165
0
2
[ "A000124", "A006000" ]
[ "M3436" ]
N. J. A. Sloane, Simon Plouffe
2025-02-16T08:32:29
oeisdata/seq/A006/A006000.seq
feff8b51932a90b3e26dfd632d188298