A376730 Expansion of (1 - x^3 - x^4)/((1 - x^3 - x^4)^2 - 4*x^7).

1, 0, 0, 1, 1, 0, 1, 6, 1, 1, 15, 15, 2, 28, 70, 29, 46, 210, 211, 111, 496, 925, 586, 1067, 3005, 3123, 2821, 8100, 13024, 11068, 20385, 44068, 48604, 57325, 129261, 192224, 200585, 358806, 662117, 781433, 1055567, 2050819, 2941702, 3524140, 6067682, 10169037

Offset: 0

Author

Seiichi Manyama, Oct 03 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A108479, A376729, A376731.

Cf. A376724, A376727.

Programs

PARI

my(N=50, x='x+O('x^N)); Vec((1-x^3-x^4)/((1-x^3-x^4)^2-4*x^7))

PARI

a(n) = sum(k=0, n\3, binomial(2*k, 2*n-6*k));

Formula

a(n) = 2*a(n-3) + 2*a(n-4) - a(n-6) + 2*a(n-7) - a(n-8).

a(n) = Sum_{k=0..floor(n/3)} binomial(2*k,2*n-6*k).