A270874 a(n) = n^10 + 9*n^9 + 53*n^8 + 218*n^7 + 695*n^6 + 1754*n^5 + 3572*n^4 + 5854*n^3 + 7510*n^2 + 6559*n + 34.
34, 26259, 294888, 2528263, 16531326, 84603579, 353479684, 1252968303, 3885899418, 10799026531, 27392790624, 64342966359, 141552806518, 294334006923, 582732259836, 1105171977919, 2017898582034, 3562049183283, 6100587181528, 10167796877991, 16534554287214
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Andrew Misseldine, Counting Schur Rings over Cyclic Groups, arXiv preprint arXiv:1508.03757 [math.RA], 2015. (page 19, 4th row; page 21, 10th row).
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Programs
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Magma
[n^10 +9*n^9 +53*n^8 +218*n^7 +695*n^6 +1754*n^5 +3572*n^4 +5854*n^3 +7510*n^2 +6559*n +34: n in [0..30]];
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Mathematica
Table[n^10 + 9 n^9 + 53 n^8 + 218 n^7 + 695 n^6 + 1754 n^5 + 3572 n^4 + 5854 n^3 + 7510 n^2 + 6559 n + 34, {n, 0, 30}] LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{34,26259,294888,2528263,16531326,84603579,353479684,1252968303,3885899418,10799026531,27392790624},30] (* Harvey P. Dale, Apr 10 2017 *) -
PARI
x='x+O('x^99); Vec((34+25885*x+7909*x^2+723130*x^3+617758*x^4+1806700*x^5+ 96940*x^6+428806*x^7-101360*x^8+25527*x^9-2529*x^10)/(1-x)^11) \\ Altug Alkan, Apr 05 2016
Formula
G.f.: (34+25885*x+7909*x^2+723130*x^3+617758*x^4+1806700*x^5+ 96940*x^6+428806*x^7-101360*x^8+25527*x^9-2529*x^10)/(1-x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).