A364589 G.f. satisfies A(x) = 1/(1-x) + x^3*A(x)^3.

1, 1, 1, 2, 4, 7, 14, 31, 67, 146, 331, 760, 1749, 4072, 9583, 22673, 53929, 129055, 310328, 749152, 1815481, 4415313, 10771564, 26352955, 64644926, 158963191, 391767016, 967523138, 2394060433, 5934576763, 14735792889, 36647185192, 91274339014, 227645446307

Offset

0,4

Links

Table of n, a(n) for n=0..33.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,2*k) * binomial(3*k,k) / (2*k+1).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n-k, 2*k)*binomial(3*k, k)/(2*k+1));

Crossrefs

Cf. A216604, A226974.

Cf. A049130, A199475, A364590.

Sequence in context: A120262 A202849 A202842 * A013326 A202973 A074663

Adjacent sequences: A364586 A364587 A364588 * A364590 A364591 A364592

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 29 2023

Status

approved