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 A360952 #9 Mar 11 2023 08:40:27
%S A360952 1,0,0,1,0,2,0,3,0,4,1,6,1,8,4,11,5,15,10,20,13,27,22,36,28,47,43,63,
%T A360952 56,82,79,107,103,140,141,180,181,232,242,299,308,380,402,483,511,613,
%U A360952 656,772,824,969,1047,1215,1309,1514,1642,1882,2039,2334,2539,2882
%N A360952 Number of strict integer partitions of n with non-integer median; a(0) = 1.
%C A360952 All of these partitions have even length.
%C A360952 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
%F A360952 a(n) = A000009(n) - A359907(n).
%e A360952 The a(0) = 1 through a(15) = 11 partitions (0 = {}, A..E = 10..14):
%e A360952 0 . . 21 . 32 . 43 . 54 4321 65 6321 76 5432 87
%e A360952 41 52 63 74 85 6431 96
%e A360952 61 72 83 94 6521 A5
%e A360952 81 92 A3 8321 B4
%e A360952 A1 B2 C3
%e A360952 5321 C1 D2
%e A360952 5431 E1
%e A360952 7321 6432
%e A360952 7431
%e A360952 7521
%e A360952 9321
%t A360952 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!IntegerQ[Median[#]]&]],{n,0,30}]
%Y A360952 The non-strict version is A307683, ranks A359912.
%Y A360952 The non-strict complement is A325347, ranks A359908.
%Y A360952 The strict complement is counted by A359907.
%Y A360952 For mean instead of median we have A361391, non-strict A349156.
%Y A360952 A000041 counts partitions, strict A000009.
%Y A360952 A008284/A058398/A327482 count partitions by mean.
%Y A360952 A067538 = partitions with integer mean, complement A102627, ranks A316413.
%Y A360952 A359893/A359901/A359902 count partitions by median.
%Y A360952 A360005(n)/2 ranks the median statistic.
%Y A360952 Cf. A000975, A051293, A082550, A240219, A240850, A327475, A359897.
%K A360952 nonn
%O A360952 0,6
%A A360952 _Gus Wiseman_, Mar 10 2023