OFFSET
0,3
COMMENTS
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..85
S. R. Finch, Monoids of natural numbers, March 17, 2009.
EXAMPLE
The subset {1,3,4,6} has 4 = 1 + 3 so is not counted under a(6).
The subset {2,3,4,5,6} has 6 = 2 + 4 and 4 = 1 + 3 so is not counted under a(6).
The a(0) = 0 through a(6) = 15 subsets:
. {1} {2} {3} {4} {5} {6}
{1,2} {1,3} {1,4} {1,5} {1,6}
{2,3} {2,4} {2,5} {2,6}
{3,4} {3,5} {3,6}
{1,2,4} {4,5} {4,6}
{2,3,4} {1,2,5} {5,6}
{1,3,5} {1,2,6}
{2,4,5} {1,3,6}
{3,4,5} {1,4,6}
{2,3,6}
{2,5,6}
{3,4,6}
{3,5,6}
{4,5,6}
{3,4,5,6}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&Intersection[#, Total/@Subsets[#, {2, Length[#]}]]=={}&]], {n, 0, 10}]
CROSSREFS
First differences of A151897.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 26 2023
EXTENSIONS
a(14) onwards added (using A151897) by Andrew Howroyd, Jan 13 2024
STATUS
approved