A284610 Number of partitions of n such that the (sum of distinct even parts) = floor(n/2).

1, 0, 0, 2, 3, 0, 0, 3, 4, 0, 0, 15, 20, 0, 0, 23, 31, 0, 0, 55, 70, 0, 0, 153, 195, 0, 0, 265, 335, 0, 0, 535, 664, 0, 0, 988, 1208, 0, 0, 2242, 2750, 0, 0, 3580, 4332, 0, 0, 6941, 8349, 0, 0, 11621, 13909, 0, 0, 20681, 24585, 0, 0, 37202

Offset: 1

Author

Clark Kimberling, Mar 30 2017

Keywords

• nonn
• easy

Examples

			a(5) counts these 3 partitions: 32, 221, 2111.
		

Crossrefs

Cf. A284608, A284616, A284617.

Programs

Mathematica

Table[p = IntegerPartitions[n];
  Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k, Length[p]}], # == Floor[n/2] &]], {n, 60}](* Peter J. C. Moses, Mar 29 2017 *)