OFFSET
0,13
COMMENTS
A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes in {a,a,b,b,b,c,d,d,d} are {b,d}.
EXAMPLE
The a(8) = 1 through a(16) = 7 partitions:
(3221) . (32221) . (4332) . (3222221) (43332) (5443)
(5331) (3322211) (53331) (6442)
(322221) (4222211) (63321) (7441)
(422211) (32222221)
(33222211)
(42222211)
(52222111)
MATHEMATICA
modes[ms_]:=Select[Union[ms], Count[ms, #]>=Max@@Length/@Split[ms]&];
Table[Length[Select[IntegerPartitions[n], !SameQ@@#&&{Mean[#]}==modes[#]&]], {n, 0, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 27 2023
STATUS
approved