A325707 Number of integer partitions of n covering an initial interval of positive integers and containing all of their distinct multiplicities.

1, 1, 0, 1, 1, 1, 2, 1, 2, 2, 4, 4, 5, 6, 7, 8, 10, 11, 13, 16, 18, 23, 26, 32, 36, 43, 48, 57, 64, 74, 84, 98, 110, 127, 145, 165, 189, 215, 244, 277, 316, 356, 403, 455, 513, 577, 650, 727, 817, 913, 1024, 1143, 1279, 1425, 1592, 1773, 1977, 2198, 2448, 2717

Offset

0,7

Comments

The Heinz numbers of these partitions are given by A325708.

Links

Table of n, a(n) for n=0..59.

Example

The initial terms count the following partitions:
   1: (1)
   3: (21)
   4: (211)
   5: (221)
   6: (321)
   6: (2211)
   7: (3211)
   8: (3221)
   8: (32111)
   9: (3321)
   9: (32211)
  10: (4321)
  10: (33211)
  10: (32221)
  10: (322111)
  11: (43211)
  11: (33221)
  11: (332111)
  11: (322211)
  12: (43221)
  12: (432111)
  12: (33321)
  12: (332211)
  12: (3222111)

Mathematica

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

Crossrefs

Cf. A000009 (partitions covering an initial interval), A055932, A109297, A114639, A114640, A290689, A324753, A325702, A325706, A325708.

Sequence in context: A324387 A163373 A117193 * A026832 A225044 A325246

Adjacent sequences: A325704 A325705 A325706 * A325708 A325709 A325710

Keyword

nonn

Author

Gus Wiseman, May 18 2019

Status

approved