A240055 Number of partitions of n such that (number of distinct parts) = m(1) - m(2), where m = multiplicity.

1, 1, 0, 0, 0, 2, 1, 1, 3, 2, 4, 5, 7, 6, 14, 11, 17, 22, 30, 28, 45, 55, 61, 78, 103, 114, 147, 183, 202, 269, 316, 372, 446, 565, 631, 778, 935, 1096, 1283, 1586, 1791, 2166, 2558, 2991, 3478, 4182, 4821, 5616, 6660, 7716, 8933, 10532, 12155, 14058, 16482

Offset

0,6

Links

Table of n, a(n) for n=0..54.

Example

a(10) counts these 4 partitions: 622, 4411, 43111, 421111.

Mathematica

z = 58; d[p_] := d[p] = Length[DeleteDuplicates[p]]; Table[Count[IntegerPartitions[n],    p_ /; d[p] == Count[p, 1] - Count[p, 2]], {n, 0, z}]

Crossrefs

Cf. A240056.

Sequence in context: A241472 A071872 A141038 * A156309 A205115 A334369

Adjacent sequences: A240052 A240053 A240054 * A240056 A240057 A240058

Keyword

nonn,easy

Author

Clark Kimberling, Mar 31 2014

Status

approved