A376788 Expansion of (1 - x^3 + x^4)/((1 - x^3 + x^4)^2 - 4*x^4).

1, 0, 0, 1, 3, 0, 1, 10, 5, 1, 21, 35, 8, 36, 126, 85, 64, 330, 463, 243, 726, 1717, 1392, 1651, 5019, 6571, 5383, 12832, 24496, 23324, 33321, 76472, 98380, 104653, 215371, 362540, 394897, 606894, 1177065, 1530509, 1899137, 3531467, 5529960, 6679652, 10503034

Offset: 0

Author

Seiichi Manyama, Oct 04 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A376716, A376787.

Cf. A376724, A376727, A376730.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\3, binomial(2*k+1, 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+1,2*n-6*k).