A284615 Number of partitions of n such that the (sum of distinct odd parts) >= n/2.

1, 1, 1, 1, 3, 4, 6, 9, 8, 11, 16, 24, 26, 37, 50, 75, 82, 113, 115, 166, 190, 259, 284, 400, 467, 619, 651, 887, 1066, 1394, 1516, 2020, 2187, 2809, 3050, 3983, 4482, 5691, 6340, 8149, 8895, 11158, 12458, 15796, 17241, 21452, 24385, 30582, 33078, 40775

Offset: 1

Author

Clark Kimberling, Apr 02 2017

Keywords

• nonn
• easy

Crossrefs

Cf. A284612, A284613, A284614.

Programs

Mathematica

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

Formula

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