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

0,7

Links

Table of n, a(n) for n=0..60.

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).

Example

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

Crossrefs

Column 3 of A373029.

Cf. A000009, A373012, A373013.

Cf. A026838, A363045.

Sequence in context: A269699 A035636 A104554 * A293304 A152414 A184834

Adjacent sequences: A372890 A372891 A372892 * A372894 A372895 A372896

Keyword

nonn

Author

Seiichi Manyama, May 20 2024

Status

approved