A270871 a(n) = n^7 + 6*n^6 + 26*n^5 + 73*n^4 + 152*n^3 + 222*n^2 + 203*n + 8.

8, 691, 5030, 25511, 100372, 324323, 898706, 2206135, 4914656, 10116467, 19506238, 35604071, 62028140, 103822051, 167841962, 263208503, 401828536, 598991795, 874047446, 1251165607, 1760188868, 2437578851, 3327462850, 4482785591, 5966571152, 7853300083

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, 7th row).

Index entries for linear recurrences with constant coefficients, signature (8,-28, 56,-70,56,-28,8,-1).

Formula

G.f.: (8 + 627*x - 274*x^2 + 4171*x^3 - 1012*x^4 + 1897*x^5 - 450*x^6 + 73*x^7)/(1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).

Mathematica

Table[n^7 + 6 n^6 + 26 n^5 + 73 n^4 + 152 n^3 + 222 n^2 + 203 n + 8, {n, 0, 40}]
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {8, 691, 5030, 25511, 100372, 324323, 898706, 2206135}, 30] (* Harvey P. Dale, Dec 17 2023 *)

Prog

(Magma) [n^7+6*n^6+26*n^5+73*n^4+152*n^3+222*n^2+203*n+8: n in [0..40]];
(PARI) x='x+O('x^99); Vec((8+627*x-274*x^2+4171*x^3-1012*x^4+1897*x^5-450*x^6+73*x^7) / (1-x)^8) \\ Altug Alkan, Apr 03 2016

Crossrefs

Cf. A270867, A270868. A270869, A270870.

Sequence in context: A202910 A332168 A168130 * A037076 A116245 A361222

Adjacent sequences: A270868 A270869 A270870 * A270872 A270873 A270874

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 03 2016

Status

approved