A375290 Expansion of 1/((1 - x + x^4)^2 + 4*x^5).

1, 2, 3, 4, 3, -4, -21, -52, -98, -144, -143, 0, 440, 1368, 2891, 4752, 5831, 3438, -7330, -33384, -81044, -148610, -211283, -197280, 39748, 732646, 2152660, 4423184, 7089816, 8360270, 4071395, -13171888, -53480919, -125422768, -224380607, -309560644, -268524883

Offset: 0

Author

Seiichi Manyama, Aug 10 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A375255, A375288.

Cf. A375293.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(1/((1-x+x^4)^2+4*x^5))

PARI

a(n) = sum(k=0, n\4, (-1)^k*binomial(2*n-6*k+2, 2*k+1))/2;

Formula

a(n) = 2*a(n-1) - a(n-2) - 2*a(n-4) - 2*a(n-5) - a(n-8).

a(n) = (1/2) * Sum_{k=0..floor(n/4)} (-1)^k * binomial(2*n-6*k+2,2*k+1).