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%I #13 Aug 27 2016 04:52:26
%S 0,1,3,4,6,7,9
%N Size of a largest subset of a regular cubic lattice of n*n*n points without repeated distances.
%C 10 <= a(7) <= 12, 11 <= a(8) <= 13, 12 <= a(9) <= 15, 13 <= a(10) <= 17.
%H Math.StackExchange, <a href="http://math.stackexchange.com/questions/1879760">A largest subset of a cubic lattice with unique distances between its points</a>, Aug 03 2016.
%H Ed Pegg Jr, <a href="http://demonstrations.wolfram.com/NoRepeatedDistances/">No Repeated Distances</a>, Wolfram Demonstrations Project, May 03 2013.
%H A. Zimmermann. <a href="http://www.azspcs.net/Contest/PointPacking/FinalReport">Al Zimmermann's Programming Contests: Point Packing</a>, Oct 10 2009.
%e For n = 5, a(5) >= 7 is witnessed by {(1,1,1), (1,1,2), (1,1,4), (1,2,5), (2,3,1), (4,4,5), (5,5,4)}. There are 4223 distinct (up to rotation and reflection) 7-point configurations without repeated distances, and none of them can be extended to 8 points, so a(5) = 7.
%Y Cf. A003022, A054578, A036501, A169942.
%K nonn,hard,more
%O 0,3
%A _Vladimir Reshetnikov_, Aug 04 2016
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