OFFSET
0,11
EXAMPLE
The strict partition (5,3,2,1) has 4 = 3 + 1 so is counted under a(11).
The a(6) = 1 through a(17) = 7 strict partitions (A..E = 10..14):
321 421 521 621 721 821 921 A21 B21 C21 D21 E21
4321 5321 6321 5431 6431 6531 7531 7631
7321 8321 7431 8431 8531
9321 A321 9431
54321 64321 B321
65321
74321
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&MemberQ[Total/@Subsets[#, {2}], 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, linear combination, or semi-sum of the parts. The current sequence is starred.
sum-full sum-free comb-full comb-free semi-full semi-free
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Triangles:
A365541 counts subsets with a semi-sum k.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 19 2023
STATUS
approved