A145137 Expansion of x/((1 - x - x^4)*(1 - x)^8).

0, 1, 9, 45, 165, 496, 1297, 3058, 6655, 13586, 26323, 48829, 87308, 151282, 255125, 420234, 678086, 1074525, 1675754, 2576688, 3912574, 5875129, 8734923, 12872391, 18820765, 27325469, 39426248, 56570687, 80771068, 114821057, 162594985

Offset: 0

Author

Alois P. Heinz, Oct 03 2008

Keywords

• nonn
• easy

Comments

The coefficients of the recursion for a(n) are given by the 9th row of A145152.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -125, 118, -56, -20, 61, -55, 28, -8, 1).

Crossrefs

9th column of A145153. Cf. A145152.

Programs

Maple

col:= proc(k) local l, j, M, n; l:= `if`(k=0, [1, 0, 0, 1], [seq(coeff( -(1-x-x^4) *(1-x)^(k-1), x, j), j=1..k+3)]); M:= Matrix(nops(l), (i,j)-> if i=j-1 then 1 elif j=1 then l[i] else 0 fi); `if`(k=0, n->(M^n)[2,3], n->(M^n)[1,2]) end: a:= col(9): seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[x/((1-x-x^4)(1-x)^8),{x,0,40}],x] (* or *) LinearRecurrence[{9,-36,84,-125,118,-56,-20,61,-55,28,-8,1},{0,1,9,45,165,496,1297,3058,6655,13586,26323,48829},40] (* Harvey P. Dale, Feb 22 2012 *)

PARI

concat(0,Vec(1/((1-x-x^4)*(1-x)^8)+O(x^99))) \\ Charles R Greathouse IV, Sep 25 2012

Formula

a(n) = [9, -36, 84, -125, 118, -56, -20, 61, -55, 28, -8, 1] * [a(n-1), ..., a(n-12)].