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

Author

Gus Wiseman, Jun 04 2019

Keywords

• nonn

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.

Examples

			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)
		

Crossrefs

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

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

Programs

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}]