A367043 G.f. satisfies A(x) = 1 + x^3 + x*A(x)^4.

1, 1, 4, 23, 144, 997, 7304, 55646, 436320, 3497846, 28538852, 236203518, 1978290648, 16735471979, 142789868112, 1227339581084, 10617748941840, 92377468226466, 807769888050640, 7095187345173620, 62574408414192220, 553881698543850337

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

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

Crossrefs

Cf. A366676, A367042.

Sequence in context: A162561 A277921 A020079 * A357152 A146964 A194006

Adjacent sequences: A367040 A367041 A367042 * A367044 A367045 A367046

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2023

Status

approved