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) = 9 partitions:
211 2111 21111 421 422 4221 631 632
3211 221111 4311 4222 5321
22111 2111111 2211111 42211 5411
211111 21111111 322111 42221
2221111 43211
22111111 332111
211111111 22211111
221111111
2111111111
For example, the partition (3,2,1,1) has maximum 3 and median 3/2, so is counted under a(7).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Max@@#==2*Median[#]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 02 2023
STATUS
approved