A284617 Number of partitions of n such that the (sum of distinct even parts) <= n/2.

1, 1, 2, 4, 6, 8, 11, 17, 23, 29, 38, 63, 81, 102, 131, 186, 235, 293, 364, 503, 622, 762, 933, 1287, 1571, 1906, 2311, 3049, 3682, 4425, 5305, 6874, 8219, 9796, 11648, 14796, 17543, 20743, 24484, 31059, 36600, 43025, 50477, 62681, 73401, 85788, 100085

Offset

1,3

Links

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

Example

a(4) counts these 4 partitions: 31, 22, 211, 1111.

Mathematica

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

Crossrefs

Cf. A284616, A284618, A284619.

Sequence in context: A374263 A338237 A039823 * A079972 A373644 A164144

Adjacent sequences: A284614 A284615 A284616 * A284618 A284619 A284620

Keyword

nonn,easy

Author

Clark Kimberling, Apr 02 2017

Status

approved