OFFSET
0,6
COMMENTS
These are partitions with at least one 1 but with fewer 1's than each of the other parts.
We define a co-mode in a multiset to be an element that appears at most as many times as each of the other elements. For example, the co-modes of {a,a,b,b,b,c,c} are {a,c}.
EXAMPLE
The a(n) partitions for n = 5, 7, 11, 13, 15:
(221) (331) (551) (661) (771)
(11111) (2221) (33221) (4441) (44331)
(1111111) (33311) (33331) (55221)
(222221) (44221) (442221)
(2222111) (332221) (3322221)
(11111111111) (2222221) (3333111)
(22222111) (22222221)
(1111111111111) (222222111)
(111111111111111)
MATHEMATICA
comodes[ms_]:=Select[Union[ms], Count[ms, #]<=Min@@Length/@Split[ms]&];
Table[Length[Select[IntegerPartitions[n], comodes[#]=={1}&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 12 2023
STATUS
approved