OFFSET
0,6
COMMENTS
We define a non-co-mode in a multiset to be an element that appears more times than at least one of the others. For example, the non-co-modes in {a,a,b,b,b,c,d,d,d} are {a,b,d}.
EXAMPLE
The a(4) = 1 through a(9) = 18 partitions:
(211) (221) (411) (322) (332) (441)
(311) (3111) (331) (422) (522)
(2111) (21111) (511) (611) (711)
(2221) (3221) (3222)
(3211) (4211) (3321)
(4111) (5111) (4221)
(22111) (22211) (4311)
(31111) (32111) (5211)
(211111) (41111) (6111)
(221111) (22221)
(311111) (33111)
(2111111) (42111)
(51111)
(321111)
(411111)
(2211111)
(3111111)
(21111111)
MATHEMATICA
ncomsi[ms_]:=Select[Union[ms], Count[ms, #]>Min@@Length/@Split[ms]&];
Table[Length[Select[IntegerPartitions[n], Length[ncomsi[#]]==1&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 18 2023
STATUS
approved