A122519 Expansion of x * (x+1) * (x^3-x^2-1) / ((x^2+1) * (x^3+x^2-1)).

1, 1, 1, 1, 1, 3, 3, 3, 5, 7, 9, 11, 15, 21, 27, 35, 47, 63, 83, 109, 145, 193, 255, 337, 447, 593, 785, 1039, 1377, 1825, 2417, 3201, 4241, 5619, 7443, 9859, 13061, 17303, 22921, 30363, 40223, 53285, 70587, 93507, 123871, 164095, 217379, 287965, 381473, 505345, 669439

Offset

1,6

Links

Table of n, a(n) for n=1..51.

Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,1).

Formula

G.f.: x*(x+1)*(x^3-x^2-1)/((x^2+1)*(x^3+x^2-1)). [Colin Barker, Oct 19 2012]

Mathematica

M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 1, 1, 0, 0}}; w[1] = {1, 1, 1, 1, 1}; w[n_] := w[n] = M.w[n - 1] a = Table[w[n][[1]], {n, 1, 30}]
LinearRecurrence[{0, 0, 1, 1, 1}, {1, 1, 1, 1, 1}, 60] (* Harvey P. Dale, Feb 02 2015 *)

Prog

(PARI) Vec(x*(x+1)*(x^3-x^2-1)/((x^2+1)*(x^3+x^2-1)) + O(x^70)) \\ Michel Marcus, Feb 12 2015

Crossrefs

Sequence in context: A290562 A346476 A307446 * A141695 A358452 A261450

Adjacent sequences: A122516 A122517 A122518 * A122520 A122521 A122522

Keyword

nonn,easy

Author

Roger L. Bagula, Sep 16 2006

Extensions

Sequence edited by Joerg Arndt, Colin Barker, Bruno Berselli, Oct 19 2012

Status

approved