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 A124943 #16 Jul 10 2023 13:08:20
%S A124943 1,1,1,2,0,1,3,1,0,1,4,2,0,0,1,6,3,1,0,0,1,8,4,2,0,0,0,1,11,6,3,1,0,0,
%T A124943 0,1,15,8,4,2,0,0,0,0,1,20,12,5,3,1,0,0,0,0,1,26,16,7,4,2,0,0,0,0,0,1,
%U A124943 35,22,10,5,3,1,0,0,0,0,0,1,45,29,14,6,4,2,0,0,0,0,0,0,1,58,40,19,8,5,3,1
%N A124943 Table read by rows: number of partitions of n with k as low median.
%C A124943 For a multiset with an odd number of elements, the low median is the same as the median. For a multiset with an even number of elements, the low median is the smaller of the two central elements.
%C A124943 Arrange the parts of a partition nonincreasing order. Remove the first part, then the last, then the first remaining part, then the last remaining part, and continue until only a single number, the low median, remains. - _Clark Kimberling_, May 16 2019
%e A124943 For the partition [2,1^2], the sole middle element is 1, so that is the low median. For [3,2,1^2], the two middle elements are 1 and 2; the low median is the smaller, 1.
%e A124943 First 8 rows:
%e A124943 1
%e A124943 1 1
%e A124943 2 0 1
%e A124943 3 1 0 1
%e A124943 4 2 0 0 1
%e A124943 6 3 1 0 0 1
%e A124943 8 4 2 0 0 0 1
%e A124943 11 6 3 1 0 0 0 1
%e A124943 From _Gus Wiseman_, Jul 09 2023: (Start)
%e A124943 Row n = 8 counts the following partitions:
%e A124943 (71) (62) (53) (44) . . . (8)
%e A124943 (611) (521) (431)
%e A124943 (5111) (422) (332)
%e A124943 (4211) (3221)
%e A124943 (41111) (2222)
%e A124943 (3311) (22211)
%e A124943 (32111)
%e A124943 (311111)
%e A124943 (221111)
%e A124943 (2111111)
%e A124943 (11111111)
%e A124943 (End)
%t A124943 Map[BinCounts[#, {1, #[[1]] + 1, 1}] &[Map[#[[Floor[(Length[#] + 2)/2]]] &, IntegerPartitions[#]]] &, Range[13]] (* _Peter J. C. Moses_, May 14 2019 *)
%Y A124943 Row sums are A000041.
%Y A124943 Column k = 1 is A027336, ranks A363488.
%Y A124943 The high version of this triangle is A124944.
%Y A124943 The rank statistic for this triangle is A363941, high version A363942.
%Y A124943 A version for mean instead of median is A363945, rank statistic A363943.
%Y A124943 A high version for mean instead of median is A363946, rank stat A363944.
%Y A124943 A version for mode instead of median is A363952, high A363953.
%Y A124943 A008284 counts partitions by length (or decreasing mean), strict A008289.
%Y A124943 A325347 counts partitions with integer median, ranks A359908.
%Y A124943 A359893 and A359901 count partitions by median.
%Y A124943 A360005(n)/2 returns median of prime indices.
%Y A124943 Cf. A025065, A026794, A027193, A067538, A237984, A240219, A362608, A363740.
%K A124943 nonn,tabl
%O A124943 1,4
%A A124943 _Franklin T. Adams-Watters_, Nov 13 2006