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A363128
Number of integer partitions of n with more than one non-co-mode.
6
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 6, 9, 18, 25, 44, 60, 96, 122, 188, 243, 344, 442, 615, 769, 1047, 1308, 1722, 2150, 2791, 3430, 4405, 5401, 6803, 8326, 10408, 12608, 15641, 18906, 23179, 27935, 34061, 40778, 49451, 59038, 71060, 84604, 101386, 120114, 143358
OFFSET
0,11
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(9) = 1 through a(12) = 9 partitions:
(32211) (33211) (33221) (43311)
(42211) (52211) (44211)
(322111) (322211) (62211)
(332111) (422211)
(422111) (522111)
(3221111) (3222111)
(3321111)
(4221111)
(32211111)
MATHEMATICA
ncomsi[ms_]:=Select[Union[ms], Count[ms, #]>Min@@Length/@Split[ms]&];
Table[Length[Select[IntegerPartitions[n], Length[ncomsi[#]]>1&]], {n, 0, 30}]
CROSSREFS
For parts instead of multiplicities we have
For middles instead of non-co-modes we have A238479, complement A238478.
For modes instead of non-co-modes we have A362607, complement A362608.
For co-modes instead of non-co-modes we have A362609, complement A362610.
For non-modes instead of non-co-modes we have A363124, complement A363125.
The complement is counted by A363129.
A000041 counts integer partitions.
A008284/A058398 count partitions by length/mean.
A362611 counts modes in prime factorization, triangle A362614.
A362613 counts co-modes in prime factorization, triangle A362615.
A363127 counts non-modes in prime factorization, triangle A363126.
A363131 counts non-co-modes in prime factorization, triangle A363130.
Sequence in context: A161338 A047847 A007783 * A050625 A025614 A182751
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 18 2023
STATUS
approved