A375288 Expansion of 1/((1 - x + x^3)^2 + 4*x^4).

1, 2, 3, 2, -5, -22, -50, -74, -47, 122, 544, 1230, 1816, 1144, -3029, -13416, -30267, -44578, -27815, 75170, 330874, 744780, 1094243, 676196, -1865344, -8160100, -18326608, -26859600, -16435947, 46284926, 201243559, 450953386, 659291863, 399432970, -1148383866

Offset: 0

Author

Seiichi Manyama, Aug 10 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A375255, A375290.

Cf. A375278, A375292.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(1/((1-x+x^3)^2+4*x^4))

PARI

a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-4*k+2, 2*k+1))/2;

Formula

a(n) = 2*a(n-1) - a(n-2) - 2*a(n-3) - 2*a(n-4) - a(n-6).

a(n) = (1/2) * Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-4*k+2,2*k+1).