OFFSET
0,10
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).
A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes of {a,a,b,b,b,c,d,d,d} are {b,d}.
EXAMPLE
The a(7) = 1 through a(13) = 17 partitions:
(3211) (4211) (3321) (5311) (4322) (4431) (4432)
(4311) (6211) (4421) (5322) (5422)
(5211) (322111) (5411) (6411) (5521)
(6311) (7311) (6322)
(7211) (8211) (6511)
(43211) (53211) (7411)
(332111) (432111) (8311)
(422111) (522111) (9211)
(54211)
(63211)
(333211)
(433111)
(442111)
(532111)
(622111)
(3322111)
(32221111)
MATHEMATICA
modes[ms_]:=Select[Union[ms], Count[ms, #]>=Max@@Length/@Split[ms]&];
Table[Length[Select[IntegerPartitions[n], Length[modes[#]]==1&&Mean[#]!=Median[#]!=First[modes[#]]&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 22 2023
STATUS
approved