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URL: https://oeis.org/A393097

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A393097
Number of partitions p of n such that max(p) > 3*min(p).
0
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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 05 2026
STATUS
approved