A376725 Expansion of 1/((1 - x^4 - x^5)^2 - 4*x^9).

1, 0, 0, 0, 2, 2, 0, 0, 3, 10, 3, 0, 4, 28, 28, 4, 5, 60, 126, 60, 11, 110, 396, 396, 117, 188, 1001, 1716, 1009, 462, 2191, 5720, 5729, 2592, 4564, 15920, 24320, 16482, 12036, 39168, 84000, 84750, 51927, 93024, 249292, 353738, 269962, 258324, 666932, 1250142

Offset: 0

Author

Seiichi Manyama, Oct 02 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A182890, A376723, A376724.

Cf. A376728, A376731.

Programs

PARI

my(N=50, x='x+O('x^N)); Vec(1/((1-x^4-x^5)^2-4*x^9))

PARI

a(n) = sum(k=0, n\4, binomial(2*k+2, 2*n-8*k+1))/2;

Formula

a(n) = 2*a(n-4) + 2*a(n-5) - a(n-8) + 2*a(n-9) - a(n-10).

a(n) = (1/2) * Sum_{k=0..floor(n/4)} binomial(2*k+2,2*n-8*k+1).