OFFSET
0,4
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(1) = 1 through a(8) = 8 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(111) (211) (221) (222) (322) (332)
(311) (411) (331) (422)
(11111) (21111) (511) (611)
(22111) (22211)
(31111) (32111)
(1111111) (41111)
(2111111)
MATHEMATICA
modes[ms_]:=Select[Union[ms], Count[ms, #]>=Max@@Length/@Split[ms]&];
Table[Length[Select[IntegerPartitions[n], Length[modes[#]]==1&&OddQ[Length[#]]&]], {n, 30}]
CROSSREFS
The constant case is A001227.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 27 2023
STATUS
approved