A240304 Number of partitions of n such that (maximal multiplicity of parts) > (multiplicity of the least part).

0, 0, 0, 0, 0, 1, 0, 2, 3, 4, 5, 12, 11, 21, 27, 37, 49, 71, 87, 124, 153, 204, 260, 344, 421, 550, 685, 867, 1076, 1360, 1660, 2081, 2544, 3145, 3831, 4706, 5692, 6958, 8395, 10171, 12224, 14761, 17645, 21204, 25281, 30207, 35914, 42760, 50618, 60057, 70914

Offset: 0

Author

Clark Kimberling, Apr 04 2014

Keywords

• nonn
• easy

Examples

			a(7) counts these 2 partitions of 7: 331, 2221.
		

Crossrefs

Cf. A240303, 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) + A240303(n) = A000041(n) for n >= 1.