A035377 Number of partitions of n into parts 6k or 6k+3.

1, 0, 0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 5, 0, 0, 7, 0, 0, 11, 0, 0, 15, 0, 0, 22, 0, 0, 30, 0, 0, 42, 0, 0, 56, 0, 0, 77, 0, 0, 101, 0, 0, 135, 0, 0, 176, 0, 0, 231, 0, 0, 297, 0, 0, 385, 0, 0, 490, 0, 0, 627, 0, 0, 792, 0, 0, 1002, 0, 0, 1255, 0, 0, 1575, 0, 0, 1958, 0, 0, 2436, 0, 0, 3010

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Comments

Euler transform of period 3 sequence [ 0, 0, 1, ...]. - Kevin T. Acres, Apr 28 2018

Crossrefs

Cf. A000041.

Programs

Maple

a:= n-> `if`(irem(n, 3)=0, combinat[numbpart](n/3), 0):
seq(a(n), n=0..84);  # Alois P. Heinz, Jun 22 2021

Mathematica

a[n_] := If[Mod[n, 3] == 0, PartitionsP[n/3], 0];
Table[a[n], {n, 0, 84}] (* Jean-François Alcover, Jan 24 2025, after Alois P. Heinz *)

Formula

a(3*n) = A000041(n). a(3*n + 1) = a(3*n + 2) = 0. - Michael Somos, Jun 02 2012