A352946 a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^k.

1, 1, 1, 1, 2, 3, 4, 6, 10, 16, 25, 42, 73, 125, 217, 391, 714, 1305, 2428, 4612, 8830, 17038, 33377, 66216, 132349, 267075, 545329, 1123693, 2333278, 4889751, 10342468, 22043954, 47340802, 102504532, 223654713, 491393646, 1087353601, 2423448817, 5437568233

Offset

0,5

Links

Table of n, a(n) for n=0..38.

Formula

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

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

Prog

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

Crossrefs

Cf. A026898, A352944.

Cf. A001840.

Sequence in context: A017986 A343304 A346075 * A342759 A293632 A216783

Adjacent sequences: A352943 A352944 A352945 * A352947 A352948 A352949

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 09 2022

Status

approved