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 A363485 #6 Jun 07 2023 08:31:48
%S A363485 0,0,0,1,0,0,2,0,0,2,2,1,3,1,2,6,5,3,8,4,8,11,13,9,17,17,19,25,24,23,
%T A363485 44,35,39,54,55,63,83,79,86,104,119,125,157,164,178,220,237,251,297,
%U A363485 324,357,413,439,486,562,607,673,765,828,901,1040,1117,1220
%N A363485 Number of integer partitions of n covering an initial interval of positive integers with more than one mode.
%C A363485 A mode in a multiset is an element that appears at least as many times as each of the others. For example, the modes of {a,a,b,b,b,c,d,d,d} are {b,d}.
%e A363485 The a(n) partitions for n = {3, 6, 12, 15, 16, 18}:
%e A363485 (21) (321) (332211) (54321) (443221) (4433211)
%e A363485 (2211) (3222111) (433221) (3332221) (5432211)
%e A363485 (22221111) (443211) (4332211) (43332111)
%e A363485 (33222111) (33322111) (333222111)
%e A363485 (322221111) (43222111) (333321111)
%e A363485 (2222211111) (3322221111)
%e A363485 (32222211111)
%e A363485 (222222111111)
%t A363485 Table[If[n==0,0,Length[Select[IntegerPartitions[n], Union[#]==Range[Max@@#]&&Length[Commonest[#]]>1&]]],{n,0,30}]
%Y A363485 For parts instead of multiplicities we have A025147, complement A096765.
%Y A363485 For co-mode we have A363264, complement A363263.
%Y A363485 The complement is counted by A363484.
%Y A363485 A000041 counts integer partitions, A000009 covering an initial interval.
%Y A363485 A071178 counts maxima in prime factorization, modes A362611.
%Y A363485 A362607 counts partitions with multiple modes, co-modes A362609.
%Y A363485 A362608 counts partitions with a unique mode, co-mode A362610.
%Y A363485 A362614 counts partitions by number of modes, co-modes A362615.
%Y A363485 Cf. A002865, A008284, A105039, A117989, A243737, A362612.
%K A363485 nonn
%O A363485 0,7
%A A363485 _Gus Wiseman_, Jun 06 2023