OFFSET
0,7
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 of {a,a,b,b,b,c,d,d,d} are {b,d}.
EXAMPLE
The a(n) partitions for n = {3, 6, 12, 15, 16, 18}:
(21) (321) (332211) (54321) (443221) (4433211)
(2211) (3222111) (433221) (3332221) (5432211)
(22221111) (443211) (4332211) (43332111)
(33222111) (33322111) (333222111)
(322221111) (43222111) (333321111)
(2222211111) (3322221111)
(32222211111)
(222222111111)
MATHEMATICA
Table[If[n==0, 0, Length[Select[IntegerPartitions[n], Union[#]==Range[Max@@#]&&Length[Commonest[#]]>1&]]], {n, 0, 30}]
CROSSREFS
The complement is counted by A363484.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 06 2023
STATUS
approved