cp's OEIS Frontend

A363128 Number of integer partitions of n with more than one non-co-mode.

%I A363128 #6 May 18 2023 08:33:30
%S A363128 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,
%T A363128 1047,1308,1722,2150,2791,3430,4405,5401,6803,8326,10408,12608,15641,
%U A363128 18906,23179,27935,34061,40778,49451,59038,71060,84604,101386,120114,143358
%N A363128 Number of integer partitions of n with more than one non-co-mode.
%C A363128 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}.
%e A363128 The a(9) = 1 through a(12) = 9 partitions:
%e A363128   (32211)  (33211)   (33221)    (43311)
%e A363128            (42211)   (52211)    (44211)
%e A363128            (322111)  (322211)   (62211)
%e A363128                      (332111)   (422211)
%e A363128                      (422111)   (522111)
%e A363128                      (3221111)  (3222111)
%e A363128                                 (3321111)
%e A363128                                 (4221111)
%e A363128                                 (32211111)
%t A363128 ncomsi[ms_]:=Select[Union[ms],Count[ms,#]>Min@@Length/@Split[ms]&];
%t A363128 Table[Length[Select[IntegerPartitions[n],Length[ncomsi[#]]>1&]],{n,0,30}]
%Y A363128 For parts instead of multiplicities we have
%Y A363128 For middles instead of non-co-modes we have A238479, complement A238478.
%Y A363128 For modes instead of non-co-modes we have A362607, complement A362608.
%Y A363128 For co-modes instead of non-co-modes we have A362609, complement A362610.
%Y A363128 For non-modes instead of non-co-modes we have A363124, complement A363125.
%Y A363128 The complement is counted by A363129.
%Y A363128 A000041 counts integer partitions.
%Y A363128 A008284/A058398 count partitions by length/mean.
%Y A363128 A362611 counts modes in prime factorization, triangle A362614.
%Y A363128 A362613 counts co-modes in prime factorization, triangle A362615.
%Y A363128 A363127 counts non-modes in prime factorization, triangle A363126.
%Y A363128 A363131 counts non-co-modes in prime factorization, triangle A363130.
%Y A363128 Cf. A002865, A053263, A098859, A237984, A275870, A327472, A353836, A353863, A359893, A362612.
%K A363128 nonn
%O A363128 0,11
%A A363128 _Gus Wiseman_, May 18 2023