%I #9 Jul 31 2015 17:49:02
%S 0,1,1,2,3,11,12,55,55,266,261,1277,1248,6121,5977,29330,28635,140531,
%T 137196,673327,657343,3226106,3149517,15457205,15090240,74059921,
%U 72301681,354842402,346418163,1700152091,1659789132,8145918055
%N a(n)= -a(n-1) +5*a(n-2) +5*a(n-3) -a(n-4) -a(n-5).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1, 5, 5, -1, -1).
%F 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]
%F a(0)=0, a(2n) = (1/3)*(A055271(n)+2).
%t 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}]
%t LinearRecurrence[{-1,5,5,-1,-1},{0,1,1,2,3},40] (* _Harvey P. Dale_, Sep 23 2012 *)
%K nonn,easy
%O 0,4
%A _Roger L. Bagula_, May 25 2005
%E Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009