A284619 Number of partitions of n such that the (sum of distinct even parts) >= n/2.

0, 1, 1, 3, 1, 3, 4, 8, 7, 13, 18, 29, 20, 33, 45, 68, 62, 92, 126, 179, 170, 240, 322, 441, 387, 530, 699, 934, 883, 1179, 1537, 2010, 1924, 2514, 3235, 4169, 4094, 5272, 6701, 8521, 7983, 10149, 12784, 16074, 15733, 19770, 24669, 30726, 29682, 36968, 45755

Offset

1,4

Comments

The number of partitions of n such that (sum distinct even parts) = n/2 is A284617(n)-A284616(n) = A284619(n)-A284618(n) = 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 15, 0, 0, 0, 23, 0, 0, 0, 55, 0, 0, 0, 153, 0, 0, 0, 265,... (offset 1, nonzero for 4|n) - R. J. Mathar, Aug 14 2023

Links

Table of n, a(n) for n=1..51.

Example

a(4) counts these 3 partitions: 4, 22, 211.

Mathematica

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

Crossrefs

Cf. A284616, A284617, A284618.

Sequence in context: A008924 A175186 A021323 * A147549 A177355 A349819

Adjacent sequences: A284616 A284617 A284618 * A284620 A284621 A284622

Keyword

nonn,easy

Author

Clark Kimberling, Apr 02 2017

Status

approved