OFFSET
0,6
COMMENTS
The non-strict version is A367218.
EXAMPLE
The a(3) = 1 through a(10) = 7 strict partitions:
(2,1) (3,1) (3,2) (4,2) (5,2) (6,2) (7,2) (8,2)
(4,1) (5,1) (6,1) (7,1) (8,1) (9,1)
(3,2,1) (4,2,1) (4,3,1) (4,3,2) (5,3,2)
(5,2,1) (5,3,1) (5,4,1)
(6,2,1) (6,3,1)
(7,2,1)
(4,3,2,1)
MATHEMATICA
combs[n_, y_]:=With[{s=Table[{k, i}, {k, y}, {i, 0, Floor[n/k]}]}, Select[Tuples[s], Total[Times@@@#]==n&]];
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&combs[Length[#], Union[#]]!={}&]], {n, 0, 15}]
CROSSREFS
The following sequences count and rank integer partitions and finite sets according to whether their length is a subset-sum or linear combination of the parts. The current sequence is starred.
sum-full sum-free comb-full comb-free
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KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 14 2023
STATUS
approved