A393986 Number of partitions p of n into distinct parts such that max(p) >= 3*min(p).

0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 7, 11, 13, 15, 19, 25, 30, 36, 43, 52, 62, 74, 88, 105, 122, 143, 168, 196, 228, 264, 307, 354, 408, 468, 537, 616, 705, 803, 916, 1043, 1185, 1343, 1521, 1719, 1943, 2192, 2471, 2783, 3126, 3509, 3937, 4411, 4937, 5520, 6167, 6883, 7677

Offset

1,6

Links

Table of n, a(n) for n=1..57.

Formula

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

Example

a(8) = 4 counts these partitions: 71, 62, 521, 431.

Crossrefs

Cf. A241063, A393970, A393971, A393985.

Cf. A241036.

Sequence in context: A339447 A027188 A363213 * A089076 A123067 A218897

Adjacent sequences: A393983 A393984 A393985 * A393987 A393988 A393989

Keyword

nonn

Author

Seiichi Manyama, Mar 05 2026

Status

approved