A122014 Expansion of -x*(8*x^7-33*x^6-30*x^5+88*x^4+35*x^3-33*x^2-11*x-1)/((x^4-x^3-3*x^2+x+1)*(x^4+x^3-3*x^2-x+1)).

1, 11, 40, 42, 179, 181, 773, 790, 3363, 3460, 14705, 15175, 64448, 66594, 282739, 292313, 1240921, 1283234, 5447271, 5633552, 23913649, 24732419, 104984728, 108581082, 460905635, 476697757, 2023486253, 2092823614, 8883609963

Offset: 1

Author

Roger L. Bagula, Sep 11 2006

Keywords

• nonn
• easy
• less

Links

• Index entries for linear recurrences with constant coefficients, signature (0, 7, 0, -13, 0, 7, 0, -1).

Programs

Mathematica

M = {{0, 1, 1, 0, 0, 1, 0, 0}, {1, 0, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}} v[1] = Table[Fibonacci[n], {n, 1, 8}] v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
LinearRecurrence[{0,7,0,-13,0,7,0,-1},{1,11,40,42,179,181,773,790},30] (* Harvey P. Dale, Jun 02 2025 *)

Formula

G.f.: -x*(8*x^7-33*x^6-30*x^5+88*x^4+35*x^3-33*x^2-11*x-1)/((x^4-x^3-3*x^2+x+1)*(x^4+x^3-3*x^2-x+1)). [Colin Barker, Aug 02 2012]

Extensions

Definition reformulated (with Barker's formula) from Joerg Arndt, Aug 02 2012