A240307 Number of partitions of n such that the m(number of distinct parts) is a part, where m = multiplicity.

0, 1, 0, 1, 1, 2, 3, 4, 6, 9, 12, 13, 23, 26, 37, 47, 67, 79, 112, 136, 180, 221, 288, 353, 450, 558, 697, 858, 1071, 1315, 1611, 1987, 2424, 2949, 3585, 4364, 5248, 6361, 7639, 9188, 11011, 13201, 15697, 18780, 22324, 26509, 31431, 37261, 43985, 51964

Offset

0,6

Links

Table of n, a(n) for n=0..49.

Example

a(6) counts these 3 partitions:  321, 2211, 1111; e.g., the number of distinct parts of 2211 is 2, which has multiplicity 2, which is a part of 2211.

Mathematica

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Count[p, Length[DeleteDuplicates[p]]]]], {n, 0, 40}]

Crossrefs

Cf. A240486.

Sequence in context: A332035 A318759 A018471 * A128166 A240470 A112249

Adjacent sequences: A240304 A240305 A240306 * A240308 A240309 A240310

Keyword

nonn,easy

Author

Clark Kimberling, Apr 07 2014

Status

approved