OFFSET
1,5
COMMENTS
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
EXAMPLE
The a(1) = 0 through a(9) = 13 partitions:
. . (21) (211) (32) (411) (43) (332) (54)
(41) (2211) (52) (611) (63)
(221) (21111) (61) (22211) (72)
(2111) (322) (41111) (81)
(2221) (221111) (441)
(4111) (2111111) (522)
(22111) (3222)
(211111) (6111)
(22221)
(222111)
(411111)
(2211111)
(21111111)
For example, the partition y = (5,3,3,2,1,1) has distinct parts {1,2,3,5}, with median 5/2, so y is counted under a(15).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !IntegerQ[Median[Union[#]]]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 22 2023
STATUS
approved