A284614 - OEIS

A284614

Number of partitions of n such that the (sum of distinct odd parts) > n/2.

1, 0, 1, 1, 3, 3, 6, 4, 8, 10, 16, 16, 26, 36, 50, 55, 82, 85, 115, 136, 190, 216, 284, 340, 467, 500, 651, 801, 1066, 1181, 1516, 1665, 2187, 2393, 3050, 3466, 4482, 5028, 6340, 6951, 8895, 9953, 12458, 13640, 17241, 19649, 24385, 26386, 33078, 36138, 44569

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OFFSET

1,5

LINKS

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

EXAMPLE

a(5) counts these 3 partitions: 5, 32, 311.

MATHEMATICA

Table[p = IntegerPartitions[n];

Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], OddQ]], {k, Length[p]}], # > n/2 &]], {n, 55}]

CROSSREFS

Cf. A284612, A284613, A284615.