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

1,2

Comments

See A366745 for the definition of contraconjugate.

Links

Table of n, a(n) for n=1..24.

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]

Crossrefs

Cf. A000041, A366745, A366745.

Sequence in context: A248782 A038714 A139554 * A230096 A116564 A323442

Adjacent sequences: A366743 A366744 A366745 * A366747 A366748 A366749

Keyword

nonn,more

Author

Clark Kimberling, Oct 25 2023

Status

approved