A284608 Number of partitions of n such that the (sum of distinct odd parts) = floor(n/2).

0, 1, 2, 0, 0, 1, 2, 5, 6, 1, 3, 8, 9, 1, 5, 20, 20, 28, 45, 30, 29, 43, 69, 60, 51, 119, 174, 86, 75, 213, 307, 355, 375, 416, 583, 517, 541, 663, 923, 1198, 1291, 1205, 1650, 2156, 2365, 1803, 2469, 4196, 4596, 4637, 6073, 6684, 7374, 6740, 8829, 12345

Offset

1,3

Links

Table of n, a(n) for n=1..56.

Example

a(8) counts these 5 partitions: 431, 3311, 3221, 32111, 311111.

Mathematica

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

Crossrefs

Cf. A284609, A284610, A284612, A284613.

Sequence in context: A361800 A340958 A320781 * A325201 A260019 A153036

Adjacent sequences: A284605 A284606 A284607 * A284609 A284610 A284611

Keyword

nonn,easy

Author

Clark Kimberling, Mar 30 2017

Status

approved