A099526 Expansion of 1/(1-2x-3x^4).

1, 2, 4, 8, 19, 44, 100, 224, 505, 1142, 2584, 5840, 13195, 29816, 67384, 152288, 344161, 777770, 1757692, 3972248, 8976979, 20287268, 45847612, 103611968, 234154873, 529171550, 1195885936, 2702607776, 6107680171, 13802874992

Offset

0,2

Comments

In general 1/(1-a*x-b*x^4) expands to sum{k=0..floor(n/4),C(n-3k,k)b^(n-3k)(a/b)^(n-4k)}.

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (2,0,0,3).

Formula

a(n)=2a(n-1)+3a(n-4); a(n)=sum{k=0..floor(n/4), binomial(n-3k, k)3^(n-3k)(2/3)^(n-4k)}.

Crossrefs

Cf. A099525.

Sequence in context: A199694 A037444 A151526 * A005703 A172383 A003081

Adjacent sequences: A099523 A099524 A099525 * A099527 A099528 A099529

Keyword

easy,nonn

Author

Paul Barry, Oct 20 2004

Status

approved