This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A363124 #9 May 17 2023 08:35:59
%S A363124 0,0,0,0,0,0,0,1,3,6,9,19,28,46,65,98,132,190,251,348,451,603,768,
%T A363124 1014,1273,1648,2052,2604,3233,4062,4984,6203,7582,9333,11349,13890,
%U A363124 16763,20388,24528,29613,35502,42660,50880,60883,72376,86158,102120,121133,143010
%N A363124 Number of integer partitions of n with more than one non-mode.
%C A363124 A non-mode in a multiset is an element that appears fewer times than at least one of the others. For example, the non-modes in {a,a,b,b,b,c,d,d,d} are {a,c}.
%e A363124 The a(7) = 1 through a(10) = 9 partitions:
%e A363124 (3211) (3221) (3321) (5221)
%e A363124 (4211) (4221) (5311)
%e A363124 (32111) (4311) (6211)
%e A363124 (5211) (32221)
%e A363124 (42111) (43111)
%e A363124 (321111) (52111)
%e A363124 (322111)
%e A363124 (421111)
%e A363124 (3211111)
%t A363124 nmsi[ms_]:=Select[Union[ms],Count[ms,#]<Max@@Length/@Split[ms]&];
%t A363124 Table[Length[Select[IntegerPartitions[n],Length[nmsi[#]]>1&]],{n,0,30}]
%Y A363124 For middle parts instead of non-modes we have A238479, complement A238478.
%Y A363124 For modes instead of non-modes we have A362607, complement A362608.
%Y A363124 For co-modes instead of non-modes we have A362609, complement A362610.
%Y A363124 The complement is counted by A363125.
%Y A363124 For non-co-modes instead of non-modes we have A363128, complement A363129.
%Y A363124 A000041 counts integer partitions.
%Y A363124 A008284/A058398 count partitions by length/mean.
%Y A363124 A362611 counts modes in prime factorization, triangle A362614.
%Y A363124 A363127 counts non-modes in prime factorization, triangle A363126.
%Y A363124 Cf. A002865, A053263, A098859, A237984, A275870, A327472, A353836, A353863, A359893, A362612.
%K A363124 nonn
%O A363124 0,9
%A A363124 _Gus Wiseman_, May 16 2023