OFFSET
0,3
COMMENTS
Also the number of maximal subsets of {1..n} containing no differences of pairs of elements. - Gus Wiseman, Jul 10 2019
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..80
N. Hindman and H. Jordan, Measures of sum-free intersecting families, New York J. Math. 13 (2007), 97-106.
EXAMPLE
a(5)=5 because the maximal sum-free subsets of {1,2,3,4,5} are {1,4}, {2,3}, {2,5}, {1,3,5} and {3,4,5}
From Gus Wiseman, Jul 10 2019: (Start)
The a(1) = 1 through a(8) = 13 subsets:
{1} {1} {1,3} {1,3} {1,4} {2,3} {1,4,6} {1,3,8}
{2} {2,3} {1,4} {2,3} {1,3,5} {1,4,7} {1,4,6}
{2,3} {2,5} {1,4,6} {2,3,7} {1,4,7}
{3,4} {1,3,5} {2,5,6} {2,5,6} {1,5,8}
{3,4,5} {3,4,5} {2,6,7} {1,6,8}
{4,5,6} {3,4,5} {2,5,6}
{1,3,5,7} {2,5,8}
{4,5,6,7} {2,6,7}
{3,4,5}
{1,3,5,7}
{2,3,7,8}
{4,5,6,7}
{5,6,7,8}
(End)
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Plus@@@Tuples[#, 2]]=={}&]]], {n, 0, 10}] (* Gus Wiseman, Jul 10 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. Hindman (nhindman(AT)aol.com), Aug 23 2006
EXTENSIONS
a(0) = 1 prepended by Gus Wiseman, Jul 10 2019
Terms a(42) and beyond from Fausto A. C. Cariboni, Oct 26 2020
STATUS
approved