A373012 Number of distinct partitions p of n such that max(p) == 1 mod 3.

0, 1, 0, 0, 1, 1, 1, 3, 2, 2, 4, 3, 4, 7, 7, 8, 12, 13, 15, 20, 21, 24, 31, 34, 39, 49, 54, 62, 76, 84, 97, 116, 130, 148, 174, 195, 221, 257, 287, 325, 374, 419, 472, 540, 604, 679, 772, 861, 966, 1092, 1218, 1362, 1533, 1706, 1903, 2133, 2368, 2635, 2943, 3263, 3622, 4033, 4463

Offset: 0

Author

Seiichi Manyama, May 20 2024

Keywords

• nonn

Examples

			a(7) = 3 counts these partitions: 7, 43, 421.
		

Crossrefs

Cf. A000009, A372893, A373013.

Programs

PARI

my(N=70, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, x^(3*k+1)*prod(j=1, 3*k, 1+x^j))))

Formula

G.f.: Sum_{k>=0} x^(3*k+1) * Product_{j=1..3*k} (1+x^j).

A000009(n) = A372893(n) + a(n) + A373013(n).