OFFSET
0,2
COMMENTS
This sequence and A085489 first differ at n = 7. a(7) = 60, A085489(7) = 61. A085489(7) includes {1, 2, 4, 7}, which is excluded from a(7) because 1+2+4 = 7.
If this sequence counts sum-free sets, A326080 counts sum-closed sets, which are different from sum-full sets (A093971). - Gus Wiseman, Jun 07 2019
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..85
EXAMPLE
a(4) = 13, including all subsets of {1, 2, 3, 4} except {1, 2, 3} (excluded
because 1+2 = 3), {1, 3, 4} (excluded because 1+3 = 4), and {1, 2, 3, 4} (excluded for both reasons.)
From Gus Wiseman, Jun 07 2019: (Start)
The a(0) = 1 through a(4) = 13 subsets:
{} {} {} {} {}
{1} {1} {1} {1}
{2} {2} {2}
{1,2} {3} {3}
{1,2} {4}
{1,3} {1,2}
{2,3} {1,3}
{1,4}
{2,3}
{2,4}
{3,4}
{1,2,4}
{2,3,4}
(End)
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], Intersection[#, Plus@@@Subsets[#, {2, Length[#]}]]=={}&]], {n, 0, 10}] (* Gus Wiseman, Jun 07 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
David Wasserman, Apr 16 2008
EXTENSIONS
a(0) = 1 prepended by Gus Wiseman, Jun 07 2019
STATUS
approved