OFFSET
0,4
FORMULA
a(n) = 2^n - A367216(n). - Chai Wah Wu, Nov 14 2023
EXAMPLE
The a(2) = 1 through a(5) = 12 subsets:
{2} {2} {2} {2}
{3} {3} {3}
{1,3} {4} {4}
{1,3} {5}
{1,4} {1,3}
{3,4} {1,4}
{1,5}
{3,4}
{3,5}
{4,5}
{1,4,5}
{2,4,5}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], FreeQ[Total/@Subsets[#], Length[#]]&]], {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
-------------------------------------------
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