A393513 Number of partitions of n having three times as many odd parts as even.

1, 0, 0, 0, 0, 1, 0, 2, 0, 4, 1, 7, 2, 11, 5, 17, 9, 25, 17, 36, 29, 51, 49, 72, 77, 101, 121, 142, 182, 199, 272, 280, 395, 394, 570, 555, 806, 779, 1133, 1093, 1571, 1526, 2166, 2124, 2957, 2942, 4017, 4055, 5416, 5559, 7274, 7583, 9712, 10285, 12921, 13881, 17112, 18635

Offset

0,8

Links

Table of n, a(n) for n=0..57.

Formula

G.f.: Sum_{k>=0} x^(5*k) / ( (Product_{j=1..k} (1-x^(2*j))) * (Product_{j=1..3*k} (1-x^(2*j))) ).

Example

a(7) counts these 2 partitions: 4111, 3211.

Crossrefs

Cf. A045931, A239258, A393514, A393515.

Sequence in context: A168036 A371499 A217930 * A305371 A355018 A177256

Adjacent sequences: A393510 A393511 A393512 * A393514 A393515 A393516

Keyword

nonn

Author

Seiichi Manyama, Feb 18 2026

Status

approved