OFFSET
0,2
FORMULA
a(n) = 2^n - A367217(n). - Chai Wah Wu, Nov 14 2023
EXAMPLE
The a(0) = 1 through a(4) = 10 subsets:
{} {} {} {} {}
{1} {1} {1} {1}
{1,2} {1,2} {1,2}
{2,3} {2,3}
{1,2,3} {2,4}
{1,2,3}
{1,2,4}
{1,3,4}
{2,3,4}
{1,2,3,4}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], MemberQ[Total/@Subsets[#], Length[#]]&]], {n, 0, 10}]
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
-------------------------------------------
A000009 counts subsets summing to n.
A000124 counts distinct possible sums of subsets of {1..n}.
Triangles:
A365541 counts sets containing two distinct elements summing to k.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Nov 12 2023
EXTENSIONS
a(16)-a(28) from Chai Wah Wu, Nov 14 2023
STATUS
approved