A366557 G.f. A(x) satisfies A(x) = 1 + x + x^3*A(x)^4.

1, 1, 0, 1, 4, 6, 8, 29, 84, 162, 360, 1074, 2808, 6444, 16464, 45629, 118244, 297450, 790184, 2138438, 5624136, 14778068, 39767024, 107287122, 286593800, 768920084, 2083170960, 5642886852, 15250029552, 41369986008, 112681853344, 306930498205, 836259756612

Offset: 0

Author

Seiichi Manyama, Oct 13 2023

Keywords

• nonn

Crossrefs

Cf. A137954, A366267, A366558.

Cf. A366594.

Programs

PARI

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

Formula

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

a(n) = A366594(n) + A366594(n-1).