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Maximum distance between a partition of n and its contraconjugate.
2

%I #4 Nov 12 2023 22:01:08

%S 1,2,2,2,2,6,6,6,8,8,12,16,20,22,30,36,42,56,68,82,118,134,160,174

%N Maximum distance between a partition of n and its contraconjugate.

%C See A366745 for the definition of contraconjugate.

%t r[n_, k_] := r[n, k] = Join[p[n, k], ConstantArray[0, n - Length[p[n, k]]]];

%t p1[n_, k_] := p1[n, k] = Reverse[IntegerPartitions[n]][[k]];

%t r1[n_, k_] := r1[n, k] = Join[p1[n, k], ConstantArray[0, n - Length[p1[n, k]]]];

%t d[u_, v_] := Total[Abs[u - v]]; (* distance function *)

%t t[n_] := Flatten[Table[d[r[n, k], r1[n, k]], {k, 1, c[n]}]];

%t t1 = Table[Count[t[n], m], {n, 1, 24}, {m, 0, 2 n - 1, 2}]; (* A366745 *)

%t Map[Max, t1]

%Y Cf. A000041, A366745, A366745.

%K nonn,more

%O 1,2

%A _Clark Kimberling_, Oct 25 2023