A370747 Number of partitions of n into distinct parts such that number of parts is a multiples of 3.

1, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 28, 31, 35, 40, 45, 51, 59, 66, 76, 87, 100, 114, 133, 151, 175, 201, 232, 265, 307, 349, 402, 458, 524, 594, 680, 767, 872, 983, 1112, 1248, 1409, 1575, 1770, 1976, 2211, 2460, 2748, 3048, 3393, 3759, 4173, 4612, 5112

Offset

0,9

Links

Table of n, a(n) for n=0..63.

Formula

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

Example

a(12) = 7 counts these partitions: 921, 831, 741, 732, 651, 642, 543.

Prog

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

Crossrefs

Cf. A000009, A067661, A372703, A373078.

Cf. A363045.

Sequence in context: A008760 A008759 A008758 * A008757 A008756 A008755

Adjacent sequences: A370744 A370745 A370746 * A370748 A370749 A370750

Keyword

nonn

Author

Seiichi Manyama, May 23 2024

Status

approved