A284611 Number of partitions of n such that the (sum of all even parts) = floor(n/2).

1, 0, 0, 1, 2, 0, 0, 4, 6, 0, 0, 12, 15, 0, 0, 30, 40, 0, 0, 70, 84, 0, 0, 165, 198, 0, 0, 330, 405, 0, 0, 704, 836, 0, 0, 1380, 1620, 0, 0, 2688, 3192, 0, 0, 4984, 5824, 0, 0, 9394, 10934, 0, 0, 16665, 19392, 0, 0, 29970, 34560, 0, 0, 52096

Offset

1,5

Links

Table of n, a(n) for n=1..60.

Example

a(8) counts these 3 partitions: 44, 431, 4111.

Mathematica

Table[p = IntegerPartitions[n];
 Length[Select[Table[Total[Select[p[[k]], EvenQ]], {k, Length[p]}], # ==
     Floor[n/2] &]], {n, 60}]

Crossrefs

Cf. A284610, A284624, A284625.

Sequence in context: A351403 A213370 A244138 * A282551 A333706 A056676

Adjacent sequences: A284608 A284609 A284610 * A284612 A284613 A284614

Keyword

nonn,easy

Author

Clark Kimberling, Mar 30 2017

Status

approved