A240450 Greatest number of distinct numbers in the intersection of p and its conjugate, as p ranges through the partitions of n.

2, 1, 3, 2, 3, 4, 3, 4, 3, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 9, 8, 9, 8, 9

Offset: 1

Author

Clark Kimberling, Apr 12 2014

Keywords

• nonn
• more

Comments

Number of terms in row n of the array at A240181.

To match the definition, all terms need to be decreased by 1 (because the rows in A240181 start with k=0). So this appears to be an incorrect duplicate of A067731. - Joerg Arndt, Jul 30 2017

Crossrefs

Cf. A067731, A240181.

Programs

Mathematica

z = 30; conjugatePartition[part_] := Table[Count[#, _?(# >= i &)], {i, First[#]}] &[part]; c = Map[BinCounts[#, {0, 1 + Max[#]}] &[Map[Length, Map[Intersection[#, conjugatePartition[#]] &, IntegerPartitions[#]]]] &, Range[z]]; Flatten[c]  (* A240181 *)
Table[Length[c[[n]]], {n, 1, z}] (* A240450 *) (* Peter J. C. Moses, Apr 10 2014 *)