OFFSET
0,2
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(7) = 12 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (32) (33) (43)
(111) (31) (41) (42) (52)
(211) (221) (51) (61)
(1111) (2111) (222) (322)
(11111) (321) (331)
(2211) (421)
(21111) (2221)
(111111) (3211)
(22111)
(211111)
(1111111)
For example, the partition y = (3,2,2) has maximum 3 and median 2, and 3 <= 2*2, so y is counted under a(7).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Max@@#<=2*Median[#]&]], {n, 30}]
CROSSREFS
For length instead of median we have A237755.
For minimum instead of median we have A237824.
For mean instead of median we have A361851.
The unequal case is A361858.
A000975 counts subsets with integer median.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 28 2023
STATUS
approved