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%I #18 Jan 04 2024 17:03:17
%S 1,1,1,3,3,6,14,20,24,36,64,110,176,238,294,370,504,736,1086,1592,
%T 2240,2982,3788,4700,5814,7322,9396,12336,16552,22192,29310,38046,
%U 48368,60078,73722,89416,108208,131310,160624,198002,247408,310410,390924,490818,613344,758518
%N Number of maximal subsets of {1..n} such that every ordered pair of distinct elements has a different difference.
%C Also the number of maximal subsets of {1..n} such that every orderless pair of (not necessarily distinct) elements has a different sum.
%H Fausto A. C. Cariboni, <a href="/A325879/b325879.txt">Table of n, a(n) for n = 0..100</a>
%e The a(0) = 1 through a(7) = 20 subsets:
%e {} {1} {1,2} {1,2} {2,3} {1,2,4} {1,2,4} {1,2,4}
%e {1,3} {1,2,4} {1,2,5} {1,2,5} {1,2,6}
%e {2,3} {1,3,4} {1,3,4} {1,2,6} {1,3,4}
%e {1,4,5} {1,3,4} {1,4,5}
%e {2,3,5} {1,3,6} {1,4,6}
%e {2,4,5} {1,4,5} {1,5,6}
%e {1,4,6} {2,3,5}
%e {1,5,6} {2,3,6}
%e {2,3,5} {2,3,7}
%e {2,3,6} {2,4,5}
%e {2,4,5} {2,4,7}
%e {2,5,6} {2,5,6}
%e {3,4,6} {2,6,7}
%e {3,5,6} {3,4,6}
%e {3,4,7}
%e {3,5,6}
%e {4,5,7}
%e {4,6,7}
%e {1,2,5,7}
%e {1,3,6,7}
%t fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t Table[Length[fasmax[Select[Subsets[Range[n]],UnsameQ@@Subtract@@@Subsets[Union[#],{2}]&]]],{n,0,10}]
%Y The subset case is A143823.
%Y The maximal case is A325879.
%Y The integer partition case is A325858.
%Y The strict integer partition case is A325876.
%Y Heinz numbers of the counterexamples are given by A325992.
%Y Cf. A002033, A108917, A143824, A196723.
%Y Cf. A325859, A325861, A325865, A325867, A325869, A325878, A325992.
%K nonn
%O 0,4
%A _Gus Wiseman_, Jun 02 2019
%E a(21)-a(45) from _Fausto A. C. Cariboni_, Feb 08 2022
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