A326036 Number of uniform complete integer partitions of n.

1, 1, 1, 2, 1, 1, 3, 2, 2, 2, 2, 2, 6, 3, 3, 5, 5, 3, 8, 5, 11, 10, 10, 9, 19, 13, 15, 17, 21, 18, 35, 26, 39, 40, 50, 50, 77, 63, 84, 88, 113, 103, 146, 132, 171, 180, 212, 214, 292, 276, 345, 363, 435, 442, 561, 569, 694, 729, 853, 891, 1108

Offset

0,4

Comments

An integer partition of n is uniform if all parts appear with the same multiplicity, and complete if every nonnegative integer up to n is the sum of some submultiset.

Links

Table of n, a(n) for n=0..60.

Example

The initial terms count the following partitions:
   0: ()
   1: (1)
   2: (11)
   3: (21)
   3: (111)
   4: (1111)
   5: (11111)
   6: (321)
   6: (2211)
   6: (111111)
   7: (421)
   7: (1111111)
   8: (3311)
   8: (11111111)
   9: (222111)
   9: (111111111)
  10: (4321)
  10: (1111111111)
  11: (5321)
  11: (11111111111)

Mathematica

sums[ptn_]:=sums[ptn]=If[Length[ptn]==1, ptn, Union@@(Join[sums[#], sums[#]+Total[ptn]-Total[#]]&/@Union[Table[Delete[ptn, i], {i, Length[ptn]}]])];
Table[Length[Select[IntegerPartitions[n], SameQ@@Length/@Split[#]&&Sort[sums[Sort[#]]]==Range[Total[#]]&]], {n, 0, 30}]

Crossrefs

Cf. A002033, A047966, A072774, A108917, A126796, A188431, A276024.

Cf. A325781, A325791, A325988, A326020, A326035, A326037.

Sequence in context: A120643 A242628 A111867 * A133776 A060118 A329143

Adjacent sequences: A326033 A326034 A326035 * A326037 A326038 A326039

Keyword

nonn

Author

Gus Wiseman, Jun 04 2019

Status

approved