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%I #14 Oct 07 2020 10:32:08
%S 1,2,3,6,9,14,21,34,49,76,101,146,205,294,397,560,747,1028,1341,1810,
%T 2343,3178,4051,5370,6921,9014,11361,14838,18719,24082,29953,38220,
%U 47663,60550,74619,93848,115961,145320,177549,221676,270335,335124
%N Number of subsets of {1,...,n + 1} containing n + 1 and such that all positive differences of distinct elements are distinct.
%C Also the number of subsets of {1...n} containing no positive differences of the elements and such that all such differences are distinct.
%H Fausto A. C. Cariboni, <a href="/A308251/b308251.txt">Table of n, a(n) for n = 0..99</a> (terms 0..41 from Gus Wiseman, terms 42..80 from Vaclav Kotesovec)
%F First differences of A143823. Partial sums of A169942.
%e The a(0) = 1 through a(5) = 14 subsets:
%e {1} {2} {3} {4} {5} {6}
%e {1,2} {1,3} {1,4} {1,5} {1,6}
%e {2,3} {2,4} {2,5} {2,6}
%e {3,4} {3,5} {3,6}
%e {1,2,4} {4,5} {4,6}
%e {1,3,4} {1,2,5} {5,6}
%e {1,4,5} {1,2,6}
%e {2,3,5} {1,3,6}
%e {2,4,5} {1,4,6}
%e {1,5,6}
%e {2,3,6}
%e {2,5,6}
%e {3,4,6}
%e {3,5,6}
%t Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&UnsameQ@@Abs[Subtract@@@Subsets[#,{2}]]&]],{n,15}]
%Y Cf. A000079, A108917, A143823, A143824, A169942, A325676, A325677, A325683, A325687.
%K nonn
%O 0,2
%A _Gus Wiseman_, May 17 2019
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