A241274 Number of partitions p of n such that (number of numbers in p that have multiplicity 1) = (number of numbers in p having multiplicity > 1).

1, 0, 0, 0, 1, 3, 3, 7, 7, 10, 12, 16, 14, 23, 25, 33, 41, 59, 72, 101, 126, 171, 216, 280, 344, 436, 535, 666, 788, 970, 1153, 1394, 1649, 1996, 2336, 2796, 3326, 3965, 4689, 5627, 6629, 7926, 9404, 11192, 13273, 15777, 18637, 22057, 26067, 30672, 36122

Offset: 0

Author

Clark Kimberling, Apr 24 2014

Keywords

• nonn
• easy

Examples

			a(6) counts these 3 partitions:  411, 3111, 21111.
		

Crossrefs

Cf. A241090, A241131, A241132.

Programs

Mathematica

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

Formula

a(n) + A329976(n) + A330001(n) = A000041(n) for n >= 0.