A352945 a(n) = Sum_{k=0..floor(n/3)} k^(n-3*k).

1, 0, 0, 1, 1, 1, 2, 3, 5, 10, 20, 42, 93, 214, 516, 1307, 3473, 9659, 28002, 84257, 262229, 842196, 2787864, 9506796, 33388393, 120727844, 449148808, 1717595949, 6743420017, 27147152525, 111931584098, 472225684599, 2037019695797, 8979468552886, 40432306870108

Offset

0,7

Links

Seiichi Manyama, Table of n, a(n) for n = 0..738

Formula

G.f.: Sum_{k>=0} x^(3*k) / (1 - k * x).

a(n) ~ sqrt(2*Pi/3) * (n/(3*LambertW(exp(1)*n/3)))^(n + 1/2 - n/LambertW(exp(1)*n/3)) / sqrt(1 + LambertW(exp(1)*n/3)). - Vaclav Kotesovec, Apr 14 2022

Prog

(PARI) a(n) = sum(k=0, n\3, k^(n-3*k));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k)/(1-k*x)))

Crossrefs

Cf. A104872, A355575.

Sequence in context: A293323 A257113 A367216 * A076834 A023170 A125312

Adjacent sequences: A352942 A352943 A352944 * A352946 A352947 A352948

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 09 2022

Status

approved