A284616 Number of partitions of n such that the (sum of distinct even parts) < n/2.

1, 1, 2, 2, 6, 8, 11, 14, 23, 29, 38, 48, 81, 102, 131, 163, 235, 293, 364, 448, 622, 762, 933, 1134, 1571, 1906, 2311, 2784, 3682, 4425, 5305, 6339, 8219, 9796, 11648, 13808, 17543, 20743, 24484, 28817, 36600, 43025, 50477, 59101, 73401, 85788, 100085

Offset

1,3

Links

Table of n, a(n) for n=1..47.

Example

a(4) counts these 2 partitions: 31, 1111.

Mathematica

Table[p = IntegerPartitions[n];
Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k,
     Length[p]}], # < n/2 &]], {n, 54}]

Crossrefs

Cf. A284617, A284618, A284619.

Sequence in context: A320248 A320067 A248823 * A136513 A365662 A214932

Adjacent sequences: A284613 A284614 A284615 * A284617 A284618 A284619

Keyword

nonn,easy

Author

Clark Kimberling, Apr 02 2017

Status

approved