A366558 G.f. A(x) satisfies A(x) = 1 + x + x^4*A(x)^4.

1, 1, 0, 0, 1, 4, 6, 4, 5, 28, 84, 140, 162, 304, 1018, 2644, 4760, 7364, 15540, 42680, 102059, 195904, 356542, 782880, 1950844, 4467288, 9011156, 17960676, 39984254, 94642292, 212395260, 444063984, 931300500, 2082762572, 4796413292, 10681800072, 22892593021

Offset: 0

Author

Seiichi Manyama, Oct 13 2023

Keywords

• nonn

Crossrefs

Cf. A137954, A366267, A366557.

Cf. A366554, A366556.

Cf. A366595.

Programs

PARI

a(n) = sum(k=0, n\4, binomial(3*k+1, n-4*k)*binomial(4*k, k)/(3*k+1));

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(3*k+1,n-4*k) * binomial(4*k,k)/(3*k+1).

a(n) = A366595(n) + A366595(n-1).