A241518 Number of partitions p of n such that #m(1) = #m(2), where #m(i) = number of numbers in p that have multiplicity i.

1, 0, 0, 1, 2, 3, 3, 4, 5, 6, 8, 12, 16, 23, 27, 41, 46, 63, 71, 96, 109, 148, 161, 219, 256, 332, 379, 500, 580, 738, 859, 1079, 1250, 1560, 1791, 2220, 2563, 3116, 3595, 4369, 5054, 6080, 7020, 8418, 9729, 11617, 13409, 15911, 18417, 21713, 25078, 29467

Offset: 0

Author

Clark Kimberling, Apr 24 2014

Keywords

• nonn
• easy

Examples

			a(6) counts these 3 partitions:  411, 222, 111111.
		

Crossrefs

Cf. A241274.

Programs

Mathematica

z = 30; u[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] == 1 &]]]; v[p_] :=  Length[DeleteDuplicates[Select[p, Count[p, #] == 2 &]]]; Table[Count[IntegerPartitions[n], p_ /; u[p] == v[p]], {n, 0, z}]