OFFSET
1,7
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(4) = 1 through a(11) = 11 partitions:
(31) (221) (321) (421) (62) (621) (442) (542)
(2221) (521) (4221) (721) (821)
(3221) (4311) (5221) (6221)
(3311) (22221) (5311) (6311)
(22211) (32211) (32221) (33221)
(33211) (42221)
(42211) (43211)
(222211) (52211)
(222221)
(322211)
(2222111)
The partition (3,2,2,2,1,1) has median 2 and minimum 1, so is counted under a(11).
The partition (5,4,2) has median 4 and minimum 2, so is counted under a(11).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], 2*Min@@#==Median[#]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 02 2023
STATUS
approved