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(8) = 16 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (21) (22) (32) (33) (43) (44)
(111) (31) (41) (42) (52) (53)
(1111) (2111) (51) (61) (62)
(11111) (222) (421) (71)
(321) (2221) (431)
(2211) (3211) (521)
(3111) (4111) (2222)
(111111) (211111) (3221)
(1111111) (3311)
(4211)
(5111)
(32111)
(221111)
(311111)
(11111111)
For example, the partition y = (3,2,2,1) has multiplicities (1,2,1), and the multiset {1,1,2} has median 1, so y is counted under a(8).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], IntegerQ[Median[Length/@Split[#]]]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 20 2023
STATUS
approved