OFFSET
1,2
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) = 1 through a(9) = 15 partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(11) (21) (22) (32) (33) (43) (44) (54)
(31) (41) (42) (52) (53) (63)
(221) (51) (61) (62) (72)
(222) (322) (71) (81)
(321) (331) (332) (333)
(421) (422) (432)
(2221) (431) (441)
(521) (522)
(2222) (531)
(3221) (621)
(3311) (3222)
(3321)
(4221)
(4311)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[#]<=2*Median[#]&]], {n, 30}]
CROSSREFS
For maximum instead of median we have A237755.
For minimum instead of median we have A237800.
For maximum instead of length we have A361848.
The equal case is A362049.
A000975 counts subsets with integer median.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 10 2023
STATUS
approved