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.
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 04 2019
STATUS
approved