A372893 Number of distinct partitions p of n such that max(p) == 0 mod 3.

1, 0, 0, 1, 1, 1, 2, 1, 1, 3, 3, 4, 6, 6, 7, 10, 11, 12, 16, 17, 20, 26, 29, 34, 42, 47, 54, 66, 74, 85, 101, 113, 129, 151, 170, 193, 224, 252, 286, 329, 370, 418, 478, 536, 603, 686, 767, 862, 974, 1088, 1218, 1370, 1527, 1704, 1910, 2124, 2366, 2643, 2934, 3260, 3631

Offset: 0

Author

Seiichi Manyama, May 20 2024

Keywords

• nonn

Examples

			a(9) = 3 counts these partitions: 9, 63, 621.
		

Crossrefs

Column 3 of A373029.

Cf. A000009, A373012, A373013.

Cf. A026838, A363045.

Formula

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

A000009(n) = a(n) + A373012(n) + A373013(n).