A114640 Number of partitions of n such that the set of parts and the set of multiplicities of parts are equal.

1, 1, 0, 0, 2, 1, 1, 0, 1, 1, 3, 2, 3, 3, 5, 0, 4, 5, 2, 3, 8, 6, 5, 10, 9, 9, 16, 14, 12, 16, 17, 10, 17, 15, 16, 19, 35, 17, 34, 37, 40, 31, 54, 36, 60, 61, 58, 63, 88, 58, 88, 87, 91, 84, 115, 93, 116, 108, 115, 130, 190, 143, 165, 214, 219, 200, 255, 240

Offset

0,5

Comments

The Heinz numbers of these partitions are given by A109297. - Gus Wiseman, Apr 02 2019

Links

Table of n, a(n) for n=0..67.

Example

From Gus Wiseman, Apr 02 2019: (Start)
The initial terms count the following integer partitions:
   0: ()
   1: (1)
   4: (22)
   4: (211)
   5: (221)
   6: (3111)
   8: (41111)
   9: (333)
  10: (511111)
  10: (3331)
  10: (322111)
  11: (332111)
  11: (322211)
  12: (6111111)
  12: (4221111)
  12: (33222)
  13: (33322)
  13: (333211)
  13: (332221)
  14: (71111111)
  14: (52211111)
  14: (4421111)
  14: (4222211)
  14: (333221)
(End)

Mathematica

Table[Length[Select[IntegerPartitions[n], Union[#]==Union[Length/@Split[#]]&]], {n, 0, 30}] (* Gus Wiseman, Apr 02 2019 *)

Crossrefs

Cf. A052335, A087153, A109297, A114639, A115584, A117144, A276429, A324572, A325132, A336031.

Sequence in context: A209354 A294446 A318163 * A056890 A321519 A346392

Adjacent sequences: A114637 A114638 A114639 * A114641 A114642 A114643

Keyword

nonn

Author

Vladeta Jovovic, Feb 18 2006

Extensions

More terms from Alois P. Heinz, Aug 09 2016

Status

approved