A145134 Expansion of x/((1 - x - x^4)*(1 - x)^5).

0, 1, 6, 21, 56, 127, 259, 490, 876, 1498, 2472, 3963, 6204, 9522, 14374, 21397, 31477, 45844, 66203, 94915, 135247, 191717, 270570, 380435, 533232, 745424, 1039745, 1447585, 2012282, 2793666, 3874331, 5368292, 7432934, 10285505, 14225881, 19667988, 27183173

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 6th row of A145152.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -14, 1, 9, -10, 5, -1).

Crossrefs

6th 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(6): seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[x / ((1 - x - x^4) (1 - x)^5), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 06 2013 *)
LinearRecurrence[{6,-15,20,-14,1,9,-10,5,-1},{0,1,6,21,56,127,259,490,876},40] (* Harvey P. Dale, Aug 14 2013 *)

PARI

concat(0,Vec(1/(1-x-x^4)/(1-x)^5+O(x^99))) \\ Charles R Greathouse IV, Sep 25 2012

Formula

a(n) = 6a(n-1) -15a(n-2) +20a(n-3) -14a(n-4) +a(n-5) +9a(n-6) -10a(n-7) +5a(n-8) -a(n-9).