OFFSET
0,3
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, 8, 12, 14, 16 (A..G = 10..16):
(6) (8) (C) (E) (G)
(33) (44) (66) (77) (88)
(222) (2222) (444) (2222222) (4444)
(111111) (3221) (3333) (3222221) (5443)
(11111111) (4332) (3322211) (6442)
(5331) (4222211) (7441)
(222222) (11111111111111) (22222222)
(322221) (32222221)
(422211) (33222211)
(111111111111) (42222211)
(52222111)
(1111111111111111)
MATHEMATICA
modes[ms_]:=Select[Union[ms], Count[ms, #]>=Max@@Length/@Split[ms]&];
Table[Length[Select[IntegerPartitions[n], {Mean[#]}==modes[#]&]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 24 2023
STATUS
approved