OFFSET

0,9

COMMENTS

A non-mode in a multiset is an element that appears fewer times than at least one of the others. For example, the non-modes in {a,a,b,b,b,c,d,d,d} are {a,c}.

EXAMPLE

The a(7) = 1 through a(10) = 9 partitions:

(3211) (3221) (3321) (5221)

(4211) (4221) (5311)

(32111) (4311) (6211)

(5211) (32221)

(42111) (43111)

(321111) (52111)

(322111)

(421111)

(3211111)

MATHEMATICA

nmsi[ms_]:=Select[Union[ms], Count[ms, #]<Max@@Length/@Split[ms]&];

Table[Length[Select[IntegerPartitions[n], Length[nmsi[#]]>1&]], {n, 0, 30}]

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 16 2023

STATUS

approved