A352986 a(n) = Sum_{k=0..floor(n/3)} k^(3*(n-3*k)).

1, 0, 0, 1, 1, 1, 2, 9, 65, 514, 4124, 33498, 281829, 2628658, 31130220, 521900363, 11550872369, 292093228523, 7763038391586, 210839178560483, 5844964107402065, 168148032885913260, 5206234971937519704, 183267822341124743772, 7684147885975909244473

Offset

0,7

Links

Table of n, a(n) for n=0..24.

Formula

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

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

Mathematica

a[0] = 1; a[n_] := Sum[k^(3*(n - 3*k)), {k, 0, Floor[n/3]}]; Array[a, 25, 0] (* Amiram Eldar, Apr 13 2022 *)

Prog

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

Crossrefs

Cf. A352945.

Sequence in context: A168383 A071300 A062395 * A099975 A292976 A334315

Adjacent sequences: A352983 A352984 A352985 * A352987 A352988 A352989

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 13 2022

Status

approved