A393097 Number of partitions p of n such that max(p) > 3*min(p).

0, 0, 0, 0, 1, 2, 4, 7, 13, 19, 30, 43, 64, 88, 123, 166, 226, 298, 394, 511, 666, 853, 1091, 1380, 1747, 2190, 2740, 3406, 4226, 5211, 6415, 7860, 9611, 11706, 14223, 17228, 20827, 25100, 30188, 36218, 43370, 51813, 61786, 73527, 87345, 103573, 122600, 144879, 170938, 201363, 236840

Offset

1,6

Links

Table of n, a(n) for n=1..51.

Formula

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

Example

a(7) = 4 counts these partitions: 61, 511, 421, 4111.

Crossrefs

Cf. A237825, A363211, A393972, A393973.

Cf. A237820.

Sequence in context: A002466 A162842 A164901 * A262744 A359516 A386400

Adjacent sequences: A393094 A393095 A393096 * A393098 A393099 A393100

Keyword

nonn

Author

Seiichi Manyama, Mar 05 2026

Status

approved