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 A360691 #5 Feb 24 2023 21:46:41
%S A360691 0,1,0,1,2,4,3,4,5,10,10,15,22,26,34,42,57,63,85,105,121,149,202,230,
%T A360691 305,355,459,544,687,778,991,1130,1396,1598,1947,2258,2761,3143,3820,
%U A360691 4412,5330,6104,7404,8499,10105,11694,13922,15917,18904,21646,25462,29213
%N A360691 Number of integer partitions of n with non-integer median of 0-prepended first differences.
%C A360691 All of these partitions have even length.
%C A360691 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
%e A360691 The a(1) = 0 through a(10) = 10 partitions:
%e A360691 . (11) . (31) (32) (33) (52) (53) (54) (55)
%e A360691 (2111) (51) (2221) (71) (72) (73)
%e A360691 (2211) (4111) (3311) (3222) (91)
%e A360691 (3111) (5111) (6111) (3322)
%e A360691 (321111) (3331)
%e A360691 (4411)
%e A360691 (5311)
%e A360691 (7111)
%e A360691 (322111)
%e A360691 (421111)
%t A360691 Table[Length[Select[IntegerPartitions[n], !IntegerQ[Median[Differences[Prepend[Reverse[#],0]]]]&]],{n,30}]
%Y A360691 For median 0 we have A360254, ranks A360558.
%Y A360691 These partitions have ranks A360557, complement A360556.
%Y A360691 The complement is counted by A360688.
%Y A360691 A000041 counts integer partitions, strict A000009.
%Y A360691 A008284 counts partitions by number of parts.
%Y A360691 A325347 counts partitions with integer median, complement A307683.
%Y A360691 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360691 Cf. A000975, A027193, A237363, A240219, A359907, A359908, A360455, A360555.
%K A360691 nonn
%O A360691 1,5
%A A360691 _Gus Wiseman_, Feb 22 2023