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 A366856 #4 Dec 23 2023 14:41:47
%S A366856 1,2,3,5,7,7,8,6,10,8,8,8,8,8,8,8,8,8,12,6,10,10,8,6,6,8,12,8,12,8,10,
%T A366856 6,8,12,10,6,10,6,8,6,8,12,8,8,8,10,8,14,14,16,12,6,8,8,10,6,12,8,8,8
%N A366856 a(n) = number of partitions p of n such that (Ferrers conjugate of p) = contraconjugate of p.
%C A366856 See A366745 for the definition of contraconjugate.
%e A366856 The partitions of 6 in reverse lexicographic order:
%e A366856 [6], [5,1], [4,2], [4,1,1], [3,3], [3,2,1], [3,1,1,1], [2,2,2], [2,2,1,1], [2,1,1,1,1], [1,1,1,1,1,1]
%e A366856 Reversed (i.e., the contraconjugates of the partitions of 6, respectively)::
%e A366856 [1,1,1,1,1,1], [2,1,1,1,1], [2,2,1,1], [2,2,2], [3,1,1,1], [3,2,1], [3,3], [4,1,1], [4,2], [5,1], [6]
%e A366856 Ferrers conjugates:
%e A366856 [1,1,1,1,1,1], [2,1,1,1,1], [2,2,1,1], [3,1,1,1], [2,2,2], [3,2,1], [4,1,1], [3,3], [4,2], [5,1], [6]
%e A366856 Comparing the 2nd and 3rd lists shows that 11-4 = 7 partitions of 6 have identical Ferrers conjugate and contraconjugate, so that a(6) = 7.
%t A366856 c[n_] := PartitionsP[n]
%t A366856 p[n_] := p[n] = IntegerPartitions[n];
%t A366856 r[n_] := r[n] = Reverse[p[n]]
%t A366856 q1[u_] := q1[u] = Table[Count[#, _?(# >= i &)], {i, First[#]}] &[u];
%t A366856 (* q1[u]=conjugate of partition u *)
%t A366856 q[n_] := q[n] = Table[q1[p[n][[k]]], {k, 1, c[n]}]
%t A366856 s[n_] := s[n] = Select[Range[c[n]], r[n][[#]] == q[n][[#]] &]
%t A366856 Table[Length[s[n]], {n, 1, 20}]
%Y A366856 Cf. A000041, A366745, A366746.
%K A366856 nonn,more
%O A366856 1,2
%A A366856 _Clark Kimberling_, Dec 05 2023