A099529 Expansion of (1+x)^2/((1+x)^2+x^3).

1, 0, 0, -1, 2, -3, 5, -9, 16, -28, 49, -86, 151, -265, 465, -816, 1432, -2513, 4410, -7739, 13581, -23833, 41824, -73396, 128801, -226030, 396655, -696081, 1221537, -2143648, 3761840, -6601569, 11584946, -20330163, 35676949, -62608681, 109870576, -192809420, 338356945, -593775046, 1042002567

Offset: 0

Author

Paul Barry, Oct 20 2004

Keywords

• easy
• sign

Comments

Binomial transform has g.f. 1/(1-x+x^3) (A050935(n+2)).

Links

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

Formula

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

a(n)=(-1)^n*A005314(n-2). [From R. J. Mathar, Nov 26 2008]