

A363264


Number of integer partitions of n covering an initial interval of positive integers with a more than one comode.


3



0, 0, 0, 1, 0, 0, 2, 1, 2, 3, 3, 2, 7, 5, 9, 12, 13, 13, 22, 19, 29, 33, 39, 43, 63, 63, 82, 94, 111, 119, 159, 164, 203, 229, 272, 301, 370, 400, 479, 538, 628, 692, 826, 904, 1053, 1181, 1353, 1502, 1742, 1919, 2205, 2456, 2790, 3097, 3539, 3911, 4435, 4929
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OFFSET

0,7


COMMENTS

We define a comode in a multiset to be an element that appears at most as many times as each of the others. For example, the comodes of {a,a,b,b,b,c,c} are {a,c}.


LINKS



MATHEMATICA

comsi[ms_]:=Select[Union[ms], Count[ms, #]<=Min@@Length/@Split[ms]&];
Table[If[n==0, 0, Length[Select[IntegerPartitions[n], Union[#]==Range[Max@@#]&&Length[comsi[#]]>1&]]], {n, 0, 30}]


CROSSREFS

For parts instead of multiplicities we have A000009, complement A087897.
For multisets instead of partitions we have A363224, complement A105039.
The complement is counted by A363263.
A000041 counts integer partitions, A000009 covering an initial interval.
A097979 counts normal multisets with a unique mode, complement A363262.


KEYWORD

nonn


AUTHOR



STATUS

approved



