A106855 Expansion of 1/(1-x^2(1-3x)).

1, 0, 1, -3, 1, -6, 10, -9, 28, -39, 55, -123, 172, -288, 541, -804, 1405, -2427, 3817, -6642, 11098, -18093, 31024, -51387, 85303, -144459, 239464, -400368, 672841, -1118760, 1873945, -3137283, 5230225, -8759118, 14642074, -24449793, 40919428, -68376015, 114268807, -191134299, 319396852

Offset: 0

Author

Paul Barry, May 08 2005

Keywords

• easy
• sign

Comments

Diagonal sums of Riordan array (1,x(1-3x)).

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,-3).

Crossrefs

Cf. A052947, A106852.

Formula

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