cp's OEIS Frontend

A363264 Number of integer partitions of n covering an initial interval of positive integers with a more than one co-mode.

%I A363264 #5 Jun 07 2023 08:31:56
%S A363264 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,
%T A363264 111,119,159,164,203,229,272,301,370,400,479,538,628,692,826,904,1053,
%U A363264 1181,1353,1502,1742,1919,2205,2456,2790,3097,3539,3911,4435,4929
%N A363264 Number of integer partitions of n covering an initial interval of positive integers with a more than one co-mode.
%C A363264 We define a co-mode in a multiset to be an element that appears at most as many times as each of the others. For example, the co-modes of {a,a,b,b,b,c,c} are {a,c}.
%t A363264 comsi[ms_]:=Select[Union[ms],Count[ms,#]<=Min@@Length/@Split[ms]&];
%t A363264 Table[If[n==0,0,Length[Select[IntegerPartitions[n],Union[#]==Range[Max@@#]&&Length[comsi[#]]>1&]]],{n,0,30}]
%Y A363264 For parts instead of multiplicities we have A000009, complement A087897.
%Y A363264 For multisets instead of partitions we have A363224, complement A105039.
%Y A363264 The complement is counted by A363263.
%Y A363264 For mode we have A363485, complement A363484.
%Y A363264 A000041 counts integer partitions, A000009 covering an initial interval.
%Y A363264 A067029 counts minima in prime factorization, co-modes A362613.
%Y A363264 A071178 counts maxima in prime factorization, modes A362611.
%Y A363264 A097979 counts normal multisets with a unique mode, complement A363262.
%Y A363264 A362607 counts partitions with multiple modes, co-modes A362609.
%Y A363264 A362608 counts partitions with a unique mode, co-mode A362610.
%Y A363264 A362614 counts partitions by number of modes, co-modes A362615.
%Y A363264 Cf. A002865, A008284, A096765, A117989, A243737, A275870, A362612.
%K A363264 nonn
%O A363264 0,7
%A A363264 _Gus Wiseman_, Jun 06 2023