A383522 a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n-2*k,k).

1, 1, 1, 4, 9, 16, 40, 99, 217, 508, 1236, 2905, 6864, 16537, 39663, 94969, 228953, 552892, 1334704, 3229545, 7828684, 18989079, 46110109, 112104531, 272771536, 664217441, 1618774405, 3947949499, 9634554687, 23526909403, 57484583145, 140529667636

Offset

0,4

Comments

Diagonal of the rational function 1 / ((1-x)*(1-y) - x*y^3).

Links

Table of n, a(n) for n=0..31.

Prog

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

Crossrefs

Cf. A000984, A002426, A383523.

Sequence in context: A111378 A106313 A219355 * A394292 A291216 A074101

Adjacent sequences: A383519 A383520 A383521 * A383523 A383524 A383525

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2025

Status

approved