A366746 Maximum distance between a partition of n and its contraconjugate.

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

Offset: 1

Author

Clark Kimberling, Oct 25 2023

Keywords

• nonn
• more

Comments

See A366745 for the definition of contraconjugate.

Crossrefs

Cf. A000041, A366745, A366745.

Programs

Mathematica

r[n_, k_] := r[n, k] = Join[p[n, k], ConstantArray[0, n - Length[p[n, k]]]];
p1[n_, k_] := p1[n, k] = Reverse[IntegerPartitions[n]][[k]];
r1[n_, k_] := r1[n, k] = Join[p1[n, k], ConstantArray[0, n - Length[p1[n, k]]]];
d[u_, v_] := Total[Abs[u - v]]; (* distance function *)
t[n_] := Flatten[Table[d[r[n, k], r1[n, k]], {k, 1, c[n]}]];
t1 = Table[Count[t[n], m], {n, 1, 24}, {m, 0, 2 n - 1, 2}];  (* A366745 *)
Map[Max, t1]