A284609 Number of partitions of n such that the (sum of all odd parts) = floor(n/2).

0, 0, 1, 1, 0, 0, 4, 4, 0, 0, 9, 12, 0, 0, 25, 30, 0, 0, 56, 70, 0, 0, 132, 165, 0, 0, 270, 330, 0, 0, 594, 704, 0, 0, 1140, 1380, 0, 0, 2268, 2688, 0, 0, 4256, 4984, 0, 0, 8008, 9394, 0, 0, 14342, 16665, 0, 0, 25920, 29970, 0, 0, 45056, 52096

Offset

1,7

Comments

Consequently the sum of all even parts is ceiling(n/2). Therefore, a(4n + 1) = a(4n + 2) = 0. - David A. Corneth, Apr 02 2017

Links

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

Example

a(8) counts these 4 partitions: 431, 3221, 32111, 311111.

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 *)

Crossrefs

Cf. A284608, A284611.

Sequence in context: A230278 A190113 A165727 * A363174 A290448 A282593

Adjacent sequences: A284606 A284607 A284608 * A284610 A284611 A284612

Keyword

nonn,easy

Author

Clark Kimberling, Mar 30 2017

Status

approved