OFFSET
1,2
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(n) partitions for n = 6, 10, 12:
(6) (10) (12)
(3,3) (5,5) (6,6)
(2,2,2) (2,2,2,2,2) (4,4,4)
(3,2,1) (3,2,2,2,1) (5,4,3)
(1,1,1,1,1,1) (4,2,2,1,1) (6,4,2)
(1,1,1,1,1,1,1,1,1,1) (7,4,1)
(3,3,3,3)
(4,3,3,2)
(5,3,3,1)
(6,3,2,1)
(2,2,2,2,2,2)
(3,2,2,2,2,1)
(3,3,2,2,1,1)
(4,2,2,2,1,1)
(1,1,1,1,1,1,1,1,1,1,1,1)
MATHEMATICA
modes[ms_]:=Select[Union[ms], Count[ms, #]>=Max@@Length/@Split[ms]&];
Table[Length[Select[IntegerPartitions[n], MemberQ[modes[#], Mean[#]]&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 24 2023
STATUS
approved