A373015 Number of partitions p of n such that max(p) == 2 mod 3.

0, 0, 1, 1, 2, 3, 4, 5, 8, 10, 14, 19, 25, 33, 45, 58, 76, 99, 127, 162, 209, 263, 333, 419, 524, 652, 813, 1003, 1239, 1524, 1868, 2281, 2786, 3382, 4104, 4965, 5993, 7213, 8676, 10396, 12447, 14866, 17725, 21087, 25063, 29711, 35185, 41589, 49089, 57839, 68079

Offset: 0

Author

Seiichi Manyama, May 20 2024

Keywords

• nonn

Examples

			a(8) = 8 counts these partitions: 8, 53, 521, 5111, 2222, 22211, 221111, 2111111.
		

Crossrefs

Cf. A000041, A363045, A373014.

Programs

PARI

my(N=60, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, N, x^(3*k+2)/prod(j=1, 3*k+2, 1-x^j))))

Formula

G.f.: Sum_{k>=0} x^(3*k+2) / Product_{j=1..3*k+2} (1-x^j).

A000041(n) = A363045(n) + A373014(n) + a(n).