A107401 a(n) = -a(n-1)+4*a(n-2)+4*a(n-3)-a(n-4)-a(n-5).

0, 1, 1, 2, 3, 8, 10, 31, 36, 117, 133, 438, 495, 1636, 1846, 6107, 6888, 22793, 25705, 85066, 95931, 317472, 358018, 1184823, 1336140, 4421821, 4986541, 16502462, 18610023, 61588028, 69453550, 229849651, 259204176, 857810577, 967363153

Offset: 0

Author

Roger L. Bagula, May 25 2005

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1, 4, 4, -1, -1).

Programs

Mathematica

n = 4 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[{-1,4,4,-1,-1},{0,1,1,2,3},40] (* Harvey P. Dale, Aug 16 2011 *)

Formula

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

a(2n) = A102871(n+1).

Extensions

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