A375470 a(n) = Sum_{k=0..floor(n/3)} (k+1) * binomial(k,n-3*k)^2.

1, 0, 0, 2, 2, 0, 3, 12, 3, 4, 36, 36, 9, 80, 180, 86, 155, 600, 607, 402, 1581, 2808, 1967, 3780, 9816, 10376, 10584, 28626, 44918, 41184, 77627, 160436, 181044, 228972, 499512, 735654, 811823, 1467072, 2640231, 3191642, 4494502, 8566308, 12280547, 15315974, 26498718

Offset

0,4

Links

Table of n, a(n) for n=0..44.

Formula

G.f.: (1-x^3-x^4)/((1-x^3-x^4)^2 - 4*x^7)^(3/2).

Prog

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

Crossrefs

Cf. A182884, A375218.

Cf. A376721.

Sequence in context: A143396 A350266 A376724 * A361893 A244129 A363907

Adjacent sequences: A375467 A375468 A375469 * A375471 A375472 A375473

Keyword

nonn

Author

Seiichi Manyama, Oct 17 2024

Status

approved