A240303 Number of partitions of n such that (maximal multiplicity of parts) = (multiplicity of the least part).

0, 1, 2, 3, 5, 6, 11, 13, 19, 26, 37, 44, 66, 80, 108, 139, 182, 226, 298, 366, 474, 588, 742, 911, 1154, 1408, 1751, 2143, 2642, 3205, 3944, 4761, 5805, 6998, 8479, 10177, 12285, 14679, 17620, 21014, 25114, 29822, 35529, 42057, 49894, 58927, 69644, 81994

Offset: 0

Author

Clark Kimberling, Apr 04 2014

Keywords

• nonn
• easy

Examples

			a(7) counts all the 15 partitions of 7 except 331 and 2221, so that a(7) = 13.
		

Crossrefs

Cf. A240304, A000041, A171979.

Programs

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n]; m[p_] := Max[Map[Length, Split[p]]] (* maximal multiplicity *)
Table[Count[f[n], p_ /; m[p] == Count[p, Min[p]]], {n, 0, z}] (* A240303 *)
Table[Count[f[n], p_ /; m[p] > Count[p, Min[p]]], {n, 0, z}] (* A240304 *)

Formula

a(n) + A240304(n) = A000041(n) for n >= 1.