A158761 a(n)=a(n-2)+64*a(n-3) with a(0)=1, a(1)=4, a(3)=16.

1, 4, 16, 68, 272, 1092, 4624, 18500, 74512, 314436, 1258512, 5083204, 21382416, 85627972, 346707472, 1454102596, 5826897680, 23643380804, 98889463824, 396564832324, 1612065835280, 6725490517060, 26992215104016

Offset

0,2

Comments

The sequence is also 2^n times the sum of the three top-row entries

of the n-th power of the matrix (0,2,0; 0,0,2;, 2,1/8,0) .

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (0, 1, 64).

Formula

G.f.: -(1+4*x+15*x^2)/(-1+x^2+64*x^3). [From R. J. Mathar, Mar 26 2009]

Mathematica

Clear[M, v, t, n];
M = {{0, t, 0}, {0, 0, t}, {t, 1/t^3, 0}};
v[0] = {1, 1, 1};
v[n_] := v[n] = M.v[n - 1];
CharacteristicPolynomial[M, x];
t = 2; a = Table[t^n*v[n][[1]], {n, 0, 30}]

Crossrefs

Sequence in context: A259815 A283036 A307051 * A179611 A290912 A089979

Adjacent sequences: A158758 A158759 A158760 * A158762 A158763 A158764

Keyword

nonn,easy

Author

Roger L. Bagula, Mar 25 2009

Extensions

Definition replaced by recurrence - The Associate Editors of the OEIS - Oct 05 2009

Status

approved