OFFSET
0,5
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 of {a,a,b,b,b,c,d,d,d} are {b,d}.
LINKS
Alois P. Heinz, Rows n = 0..800, flattened
FORMULA
EXAMPLE
Triangle begins:
1
0 1
0 2
0 2 1
0 4 1
0 5 2
0 7 3 1
0 11 3 1
0 16 4 2
0 21 6 3
0 29 8 4 1
0 43 7 5 1
0 54 13 8 2
0 78 12 8 3
0 102 17 11 5
0 131 26 12 6 1
0 175 29 17 9 1
Row n = 8 counts the following partitions:
(8) (53) (431)
(44) (62) (521)
(332) (71)
(422) (3311)
(611)
(2222)
(3221)
(4211)
(5111)
(22211)
(32111)
(41111)
(221111)
(311111)
(2111111)
(11111111)
MATHEMATICA
msi[ms_]:=Select[Union[ms], Count[ms, #]>=Max@@Length/@Split[ms]&];
Table[Length[Select[IntegerPartitions[n], Length[msi[#]]==k&]], {n, 0, 15}, {k, 0, Floor[(Sqrt[1+8n]-1)/2]}]
CROSSREFS
KEYWORD
AUTHOR
Gus Wiseman, May 04 2023
STATUS
approved