A239964 Number of partitions of n such that (number of distinct parts) = maximal multiplicity of the parts.

0, 1, 1, 1, 2, 3, 3, 4, 6, 5, 11, 12, 15, 21, 26, 30, 41, 52, 56, 82, 99, 118, 144, 189, 221, 279, 327, 405, 491, 600, 699, 860, 1038, 1230, 1470, 1754, 2106, 2487, 2970, 3489, 4148, 4883, 5779, 6763, 8024, 9284, 11006, 12780, 15029, 17452, 20405, 23660

Offset: 0

Author

Clark Kimberling, Mar 30 2014

Keywords

• nonn
• easy

Examples

			a(8) counts these partitions:  8, 611, 422, 332, 3311, 32111.
		

Crossrefs

Cf. A239948, A239966.

Programs

Mathematica

z = 58; d[p_] := d[p] = Length[DeleteDuplicates[p]]; m[p_] := Max[Map[Length, Split[p]]]; Table[Count[IntegerPartitions[n], p_ /; d[p] == m[p]], {n, 0, z}]