A363066 Number of partitions p of n such that (1/3)*max(p) is a part of p.

1, 0, 0, 0, 1, 1, 2, 3, 5, 6, 9, 11, 16, 20, 27, 33, 45, 55, 72, 89, 116, 142, 181, 222, 281, 343, 429, 522, 649, 786, 967, 1168, 1429, 1719, 2088, 2504, 3026, 3615, 4345, 5174, 6192, 7349, 8755, 10360, 12297, 14507, 17154, 20182, 23788, 27910, 32790, 38374, 44955, 52480, 61307, 71402

Offset

0,7

Links

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

Formula

G.f.: Sum_{k>=0} x^(4*k)/Product_{j=1..3*k} (1-x^j).

Example

a(7) = 3 counts these partitions:  331, 3211, 31111.

Prog

(PARI) a(n) = sum(k=0, n\4, #partitions(n-4*k, 3*k));

Crossrefs

Cf. A002865, A238479, A363067, A363068.

Cf. A008484, A237825, A363045.

Sequence in context: A027588 A224956 A131995 * A060714 A241819 A227070

Adjacent sequences: A363063 A363064 A363065 * A363067 A363068 A363069

Keyword

nonn

Author

Seiichi Manyama, May 16 2023

Status

approved