A119886 a(n) = 20*a(n-2) - 64*a(n-4).

1, 59, 2416, 6230, 47680, 120824, 798976, 2017760, 12928000, 32622464, 207425536, 523312640, 3321118720, 8378415104, 53147140096, 134076293120, 850391203840, 2145307295744, 13606407110656, 34325263155200, 217703105167360, 549205596176384, 3483252048265216

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,20,0,-64).

Formula

G.f.: -(576*x^4-5050*x^3-2396*x^2-59*x-1) / ((2*x-1)*(2*x+1)*(4*x-1)*(4*x+1)). - Colin Barker, Nov 17 2012

a(n) = 2^(n-4)*(-3266 + 585*(-2)^n + 258*(-1)^n + 2583*2^n) for n>0. - Colin Barker, Feb 05 2017

Mathematica

M = {{0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0}, {1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0}} v[1] = Table[Fibonacci[n], {n, 1, 16}] v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
(* Second program: *)
A = SparseArray[{{1, 8} -> 1, Band[{1, 4}] -> 1, Band[{1, 2}, {3, 4}] -> 1, Band[{5, 6}, {7, 8}] -> 1}, {8, 8}]; M = ArrayFlatten[{{A+Transpose[A], IdentityMatrix[8]}, {IdentityMatrix[8], A+Transpose[A]}}]; v[1] = Array[ Fibonacci, 16]; v[n_] := v[n] = M.v[n-1]; A119886 = Array[v, 50][[All, 1]] (* Jean-François Alcover, Feb 05 2017 *)

Prog

(PARI) Vec(-(576*x^4-5050*x^3-2396*x^2-59*x-1) / ((2*x-1)*(2*x+1)*(4*x-1)*(4*x+1)) + O(x^30)) \\ Colin Barker, Feb 05 2017

Crossrefs

Cf. A060595, A060638, A002409, A099193, A000937, A099195.

Sequence in context: A017775 A017722 A263508 * A135649 A278367 A198509

Adjacent sequences: A119883 A119884 A119885 * A119887 A119888 A119889

Keyword

nonn,easy

Author

Roger L. Bagula, Aug 09 2006

Extensions

New name from Joerg Arndt, Feb 05 2017

Status

approved