A097116 Expansion of (1-x)/((1-x)^2-3x^3).

1, 1, 1, 4, 10, 19, 40, 91, 199, 427, 928, 2026, 4405, 9568, 20809, 45265, 98425, 214012, 465394, 1012051, 2200744, 4785619, 10406647, 22629907, 49210024, 107010082, 232699861, 506019712, 1100369809, 2392819489, 5203328305

Offset: 0

Author

Paul Barry, Jul 25 2004

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (2, -1, 3).

Formula

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