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%I #6 Jun 02 2019 23:40:53
%S 1,1,2,2,4,8,8,10,18,34,50,70,78,89,120,181,277,401,561,728,867,1031,
%T 1219,1537
%N Number of maximal subsets of {1..n} containing n such that every ordered pair of distinct elements has a different difference.
%C Also the number of maximal subsets of {1..n} containing n such that every orderless pair of (not necessarily distinct) elements has a different sum.
%e The a(2) = 1 through a(9) = 18 subsets:
%e {1,2} {1,3} {1,2,4} {1,2,5} {1,2,6} {2,3,7} {3,5,8} {4,6,9}
%e {2,3} {1,3,4} {1,4,5} {1,3,6} {2,4,7} {4,5,8} {5,6,9}
%e {2,3,5} {1,4,6} {2,6,7} {1,2,4,8} {1,2,4,9}
%e {2,4,5} {1,5,6} {3,4,7} {1,2,6,8} {1,2,6,9}
%e {2,3,6} {4,5,7} {1,3,4,8} {1,2,7,9}
%e {2,5,6} {4,6,7} {1,3,7,8} {1,3,4,9}
%e {3,4,6} {1,2,5,7} {1,5,6,8} {1,3,8,9}
%e {3,5,6} {1,3,6,7} {1,5,7,8} {1,4,8,9}
%e {2,3,6,8} {1,6,7,9}
%e {2,4,7,8} {1,6,8,9}
%e {2,3,5,9}
%e {2,3,7,9}
%e {2,4,5,9}
%e {2,4,8,9}
%e {2,6,7,9}
%e {2,6,8,9}
%e {3,4,7,9}
%e {3,5,8,9}
%t fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t Table[Length[fasmax[Select[Subsets[Range[n]],MemberQ[#,n]&&UnsameQ@@Subtract@@@Subsets[Union[#],{2}]&]]],{n,0,10}]
%Y Cf. A002033, A108917, A143823, A143824, A196723.
%Y Cf. A325858, A325859, A325861, A325867, A325869, A325879, A325992.
%K nonn,more
%O 1,3
%A _Gus Wiseman_, Jun 02 2019