OFFSET
0,5
COMMENTS
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..88
S. R. Finch, Monoids of natural numbers, March 17, 2009.
FORMULA
First differences of A093971.
EXAMPLE
The subset {1,3} has no element equal to the sum of two others, so is not counted under a(3).
The subset {3,4,5} has no element equal to the sum of two others, so is not counted under a(5).
The subset {1,3,4} has 4 = 1 + 3, so is counted under a(4).
The subset {2,4,5} has 4 = 2 + 2, so is counted under a(5).
The a(0) = 0 through a(5) = 9 subsets:
. . {1,2} {1,2,3} {2,4} {1,2,5}
{1,2,4} {1,4,5}
{1,3,4} {2,3,5}
{2,3,4} {2,4,5}
{1,2,3,4} {1,2,3,5}
{1,2,4,5}
{1,3,4,5}
{2,3,4,5}
{1,2,3,4,5}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&Intersection[#, Total /@ Tuples[#, 2]]!={}&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 24 2023
EXTENSIONS
a(21) onwards added (using A093971) by Andrew Howroyd, Jan 13 2024
STATUS
approved