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A114640 Number of partitions of n such that the set of parts and the set of multiplicities of parts are equal. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 22:08 EST 2022. Contains 350480 sequences. (Running on oeis4.)