A363067 Number of partitions p of n such that (1/4)*max(p) is a part of p.

1, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 31, 39, 51, 64, 81, 102, 128, 159, 198, 245, 304, 374, 460, 563, 689, 841, 1023, 1242, 1505, 1819, 2195, 2642, 3173, 3804, 4551, 5435, 6477, 7707, 9151, 10850, 12843, 15175, 17902, 21089, 24802, 29132, 34164, 40012, 46796, 54663, 63766

Offset

0,8

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: Sum_{k>=0} x^(5*k)/Product_{j=1..4*k} (1-x^j).

Example

a(8) = 3 counts these partitions:  431, 4211, 41111.

Prog

(PARI) a(n) = sum(k=0, n\5, #partitions(n-5*k, 4*k));

Crossrefs

Cf. A002865, A238479, A363066, A363068.

Cf. A237826, A363046.

Sequence in context: A377076 A347549 A008628 * A038499 A118199 A239883

Adjacent sequences: A363064 A363065 A363066 * A363068 A363069 A363070

Keyword

nonn

Author

Seiichi Manyama, May 16 2023

Status

approved