A275672 Size of a largest subset of a regular cubic lattice of n*n*n points without repeated distances.

0, 1, 3, 4, 6, 7, 9

Offset: 0

Author

Vladimir Reshetnikov, Aug 04 2016

Keywords

• nonn
• hard
• more

Comments

10 <= a(7) <= 12, 11 <= a(8) <= 13, 12 <= a(9) <= 15, 13 <= a(10) <= 17.

Examples

			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.
		

Links

• Math.StackExchange, A largest subset of a cubic lattice with unique distances between its points, Aug 03 2016.
• Ed Pegg Jr, No Repeated Distances, Wolfram Demonstrations Project, May 03 2013.
• A. Zimmermann. Al Zimmermann's Programming Contests: Point Packing, Oct 10 2009.

Crossrefs

Cf. A003022, A054578, A036501, A169942.