A352982 a(n) = Sum_{k=0..floor(n/3)} k^n.

1, 0, 0, 1, 1, 1, 65, 129, 257, 20196, 60074, 179196, 17312754, 68711380, 273234810, 31605701625, 156925970179, 780248593545, 105443761093411, 628709267031321, 3752628871164355, 580964060390826448, 4043844561787569140, 28170468954985342384

Offset: 0

Author

Seiichi Manyama, Apr 13 2022

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..458

Crossrefs

Cf. A089072, A352945, A352981.

Programs

Magma

[(&+[k^n: k in [0..Floor(n/3)]]): n in [0..40]]; // G. C. Greubel, Nov 01 2022

Mathematica

a[0] = 1; a[n_] := Sum[k^n, {k, 0, Floor[n/3]}]; Array[a, 24, 0] (* Amiram Eldar, Apr 13 2022 *)

PARI

a(n) = sum(k=0, n\3, k^n);

PARI

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

SageMath

[sum( k^n for k in range((n//3)+1)) for n in range(41)] # G. C. Greubel, Nov 01 2022

Formula

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