A239959 Number of partitions of n such that 2*(number of distinct parts) = number of parts.

1, 0, 1, 0, 1, 1, 3, 2, 3, 3, 8, 8, 11, 14, 19, 19, 29, 37, 47, 61, 79, 85, 114, 141, 168, 210, 257, 309, 395, 468, 556, 685, 816, 966, 1162, 1380, 1667, 1988, 2340, 2777, 3305, 3900, 4571, 5423, 6348, 7385, 8700, 10188, 11846, 13876, 16118, 18757, 21846

Offset: 0

Author

Clark Kimberling, Mar 30 2014

Keywords

• nonn
• easy

Examples

			a(10) counts these 8 partitions:  7111, 55, 4411, 4222, 421111, 3331, 3322, 322111.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A239954.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
     `if`(i<1, 0, add(b(n-i*j, i-1, t+`if`(j>0, 2, 0)-j), j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..60);

Mathematica

z = 55; d[p_] := d[p] = Length[DeleteDuplicates[p]]; Table[Count[IntegerPartitions[n], p_ /; 2*d[p] == Length[p]], {n, 0, z}]