A239945 Number of partitions of n containing the number of distinct parts as a part.

0, 1, 1, 2, 2, 4, 5, 7, 10, 14, 19, 24, 35, 43, 61, 74, 100, 127, 165, 207, 268, 330, 423, 528, 653, 822, 1012, 1247, 1535, 1898, 2296, 2823, 3432, 4161, 5025, 6109, 7311, 8840, 10578, 12680, 15157, 18102, 21496, 25612, 30402, 35957, 42564, 50288, 59259

Offset

0,4

Links

Table of n, a(n) for n=0..48.

Formula

a(n) + A239946(n) = A000041(n) for n >= 0.

Example

a(9) counts these 14 partitions:  72, 531, 522, 432, 4311, 3321, 3222, 32211, 321111, 22221, 222111, 2211111, 21111111, 111111111.

Mathematica

z = 55; d[p_] := d[p] = Length[DeleteDuplicates[p]];
t = Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, d[p]]], {n, 0, z}]
(* A239945 *)
Table[PartitionsP[n] - t[[n + 1]], {n, 0, z}] (* A239946 *)

Crossrefs

Cf. A239946.

Sequence in context: A323092 A238594 A350837 * A363740 A238875 A344740

Adjacent sequences: A239942 A239943 A239944 * A239946 A239947 A239948

Keyword

nonn,easy

Author

Clark Kimberling, Mar 30 2014

Status

approved