A270872 a(n) = n^8 + 7*n^7 + 34*n^6 + 111*n^5 + 275*n^4 + 511*n^3 + 703*n^2 + 623*n + 13.

13, 2278, 19439, 117910, 550009, 2072078, 6584443, 18269614, 45445445, 103390294, 218437543, 433677158, 816642289, 1469399230, 2541499379, 4246292158, 6881138173, 10852102214, 16703746015, 25154681014, 37139581673, 53858400238, 76833564139, 107975977550

Offset

0,1

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, 8th row).

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: (13+2161*x-595*x^2+23875*x^3-1091*x^4+19271*x^5-4997*x^6+1909*x^7-226*x^8)/(1-x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).

Mathematica

Table[n^8 + 7 n^7 + 34 n^6 + 111 n^5 + 275 n^4 + 511 n^3 + 703 n^2 + 623 n + 13, {n, 0, 40}]
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {13, 2278, 19439, 117910, 550009, 2072078, 6584443, 18269614, 45445445}, 30] (* Harvey P. Dale, Jan 14 2023 *)

Prog

(Magma) [n^8+7*n^7+34*n^6+111*n^5+275*n^4+511*n^3+703*n^2+623*n+13: n in [0..40]];
(PARI) x='x+O('x^99); Vec((13+2161*x-595*x^2+23875*x^3-1091*x^4+19271*x^5-4997*x^6+1909*x^7-226*x^8)/(1-x)^9) \\ Altug Alkan, Apr 04 2016

Crossrefs

Cf. A270867, A270868, A270869, A270870, A270871.

Sequence in context: A145187 A221896 A209468 * A141077 A202517 A221901

Adjacent sequences: A270869 A270870 A270871 * A270873 A270874 A270875

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 04 2016

Status

approved