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

0,7

Links

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

Example

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

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}]

Crossrefs

Cf. A239954.

Sequence in context: A106151 A323467 A341097 * A214435 A215926 A007888

Adjacent sequences: A239956 A239957 A239958 * A239960 A239961 A239962

Keyword

nonn,easy

Author

Clark Kimberling, Mar 30 2014

Status

approved