A376729 Expansion of (1 - x^2 - x^3)/((1 - x^2 - x^3)^2 - 4*x^5).

1, 0, 1, 1, 1, 6, 2, 15, 16, 29, 71, 73, 212, 276, 541, 1016, 1497, 3189, 4825, 9162, 16022, 26763, 50424, 82869, 151851, 262705, 456520, 820328, 1401913, 2511824, 4361521, 7657481, 13528913, 23509678, 41633002, 72630919, 127709888, 224418509, 392539055, 691382201

Offset: 0

Author

Seiichi Manyama, Oct 03 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A108479, A376730, A376731.

Cf. A376723, A376726.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec((1-x^2-x^3)/((1-x^2-x^3)^2-4*x^5))

PARI

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

Formula

a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6).

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