A107402 a(n)= -a(n-1) +5*a(n-2) +5*a(n-3) -a(n-4) -a(n-5).

0, 1, 1, 2, 3, 11, 12, 55, 55, 266, 261, 1277, 1248, 6121, 5977, 29330, 28635, 140531, 137196, 673327, 657343, 3226106, 3149517, 15457205, 15090240, 74059921, 72301681, 354842402, 346418163, 1700152091, 1659789132, 8145918055

Offset: 0

Author

Roger L. Bagula, May 25 2005

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (-1, 5, 5, -1, -1).

Programs

Mathematica

m = 5 M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {-1, -1, m, m, -1}} Expand[Det[M - x*IdentityMatrix[5]]] NSolve[Det[M - x*IdentityMatrix[5]] == 0, x] v[1] = {0, 1, 1, 2, 3} digits = 50 v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, digits}]
LinearRecurrence[{-1,5,5,-1,-1},{0,1,1,2,3},40] (* Harvey P. Dale, Sep 23 2012 *)

Formula

G.f.: -x*(5*x^3+2*x^2-2*x-1)/((x+1)*(x^4-5*x^2+1)). [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]

a(0)=0, a(2n) = (1/3)*(A055271(n)+2).

Extensions

Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009