A099493 Expansion of (1+x^2)^2/(1+x^2-2x^3+x^4+x^6).

1, 0, 1, 2, -1, 0, 3, -4, -3, 8, -7, -10, 23, -8, -33, 56, 1, -104, 121, 58, -297, 232, 291, -780, 349, 1072, -1903, 174, 3407, -4272, -1505, 9840, -8543, -8752, 26321, -13902, -33777, 65456, -11805, -110356, 150173, 35192, -325303, 310054, 257319, -885496, 537919, 1054888, -2240927

Offset: 0

Author

Paul Barry, Oct 19 2004

Keywords

• easy
• sign

Comments

A Chebyshev transform of A052907, which has g.f. 1/(1-2x^2-2x^3). The image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).

Links

• Index entries for linear recurrences with constant coefficients, signature (0,-1,2,-1,0,-1).

Formula

a(n)=-a(n-2)+2a(n-3)-a(n-4)-a(n-6); a(n)=sum{k=0..floor(n/2), C(n-k, k)(-1)^k*sum{j=0.., floor(n-2k/2), C(j, n-2k-2j)2^j}}.