A324572 Number of integer partitions of n whose multiplicities (where if x < y the multiplicity of x is counted prior to the multiplicity of y) are equal to the distinct parts in decreasing order.

1, 1, 0, 0, 2, 0, 1, 0, 1, 1, 2, 0, 3, 0, 2, 0, 4, 1, 2, 1, 4, 1, 3, 1, 5, 3, 5, 1, 6, 2, 6, 1, 7, 2, 7, 2, 11, 4, 8, 3, 11, 5, 10, 4, 13, 5, 11, 5, 16, 8, 14, 5, 19, 8, 18, 6, 22, 8, 22, 7, 26, 10, 25, 8, 33, 12, 29, 11, 36, 13, 34, 12, 40, 16, 41, 14, 47, 17, 45, 16, 55

Offset

0,5

Comments

These are a kind of self-describing partitions (cf. A001462, A304679).

The Heinz numbers of these partitions are given by A324571.

The case where the distinct parts are taken in increasing order is counted by A033461, with Heinz numbers given by A109298.

Links

Table of n, a(n) for n=0..80.

Example

The first 19 terms count the following integer partitions:
   1: (1)
   4: (22)
   4: (211)
   6: (3111)
   8: (41111)
   9: (333)
  10: (511111)
  10: (322111)
  12: (6111111)
  12: (4221111)
  12: (33222)
  14: (71111111)
  14: (52211111)
  16: (811111111)
  16: (622111111)
  16: (4444)
  16: (442222)
  17: (43331111)
  18: (9111111111)
  18: (7221111111)
  19: (533311111)

Mathematica

Table[Length[Select[IntegerPartitions[n], Union[#]==Length/@Split[#]&]], {n, 0, 30}]

Crossrefs

Cf. A001156, A033461, A109298, A117144, A276078, A324524, A324571.

Sequences related to self-description: A000002, A001462, A079000, A079254, A276625, A304360.

Sequence in context: A292342 A091991 A108234 * A153148 A378437 A091830

Adjacent sequences: A324569 A324570 A324571 * A324573 A324574 A324575

Keyword

nonn

Author

Gus Wiseman, Mar 08 2019

Extensions

More terms from Alois P. Heinz, Mar 08 2019

Status

approved