OFFSET
1,8
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). All of these partitions have even length, because an odd-length multiset cannot have fractional median.
EXAMPLE
The a(13) = 3 through a(15) = 5 partitions:
(7,2,2,2) (8,2,2,2) (9,2,2,2)
(8,2,2,1) (9,2,2,1) (10,2,2,1)
(8,3,1,1) (9,3,1,1) (10,3,1,1)
(3,3,3,3,1,1) (3,3,3,3,2,1)
(4,3,3,3,1,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[#]==2*Median[#]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 10 2023
STATUS
approved