A099525 Expansion of 1/(1-2x-3x^3).

1, 2, 4, 11, 28, 68, 169, 422, 1048, 2603, 6472, 16088, 39985, 99386, 247036, 614027, 1526212, 3793532, 9429145, 23436926, 58254448, 144796331, 359903440, 894570224, 2223529441, 5526769202, 13737249076, 34145086475, 84870480556

Offset: 0

Author

Paul Barry, Oct 20 2004

Keywords

• easy
• nonn

Comments

In general 1/(1-a*x-b*x^3) expands to sum{k=0..floor(n/3),C(n-2k,k)b^(n-2k)(a/b)^(n-3k)}.

Links

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

Formula

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