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A284612
Number of partitions of n such that the (sum of distinct odd parts) < n/2.
4
0, 1, 2, 4, 4, 7, 9, 13, 22, 31, 40, 53, 75, 98, 126, 156, 215, 272, 375, 461, 602, 743, 971, 1175, 1491, 1817, 2359, 2831, 3499, 4210, 5326, 6329, 7956, 9501, 11833, 13994, 17155, 20324, 24845, 29189, 35688, 42016, 50803, 59379, 71893, 84106, 100369, 116691
OFFSET
1,3
EXAMPLE
a(6) counts these 7 partitions: 6, 41, 411, 222, 2211, 21111, 111111.
MATHEMATICA
Table[p = IntegerPartitions[n];
Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], OddQ]], {k, Length[p]}], # < n/2 &]], {n, 55}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 30 2017
STATUS
approved