A284612 Number of partitions of n such that the (sum of distinct odd parts) < n/2.

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

Links

Table of n, a(n) for n=1..48.

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

Cf. A284613, A284614, A284615.

Sequence in context: A262884 A340448 A241387 * A070072 A265259 A238493

Adjacent sequences: A284609 A284610 A284611 * A284613 A284614 A284615

Keyword

nonn,easy

Author

Clark Kimberling, Mar 30 2017

Status

approved