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A326036
Number of uniform complete integer partitions of n.
6
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.
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 04 2019
STATUS
approved