OFFSET
0,7
EXAMPLE
The strict partition (6,4,3,2,1) has submultisets {1,4} and {2,3} with sum 5 so is counted under a(16).
The a(1) = 1 through a(10) = 5 strict partitions:
(1) . (2,1) . (3,2) (4,2) (5,2) (6,2) (7,2) (8,2)
(3,2,1) (4,2,1) (4,3,1) (4,3,2) (5,3,2)
(5,2,1) (5,3,1) (6,3,1)
(6,2,1) (7,2,1)
(4,3,2,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&MemberQ[Total/@Subsets[#], Length[#]]&]], {n, 0, 30}]
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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Triangles:
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 12 2023
STATUS
approved