Neil Sloane <njasloane@gmail.com> wrote:
I don't have the answer to your question, but I have some suggestions.
. . . %N A193838 Size k of smallest square of k X k lattice points from which n points with distinct mutual distances can be chosen.
Thanks. That's the inverse function: 1,2,3,4,5,6,7,9,10,12,14,... Since my function is monotonic, it's uniquely specified by yours. Mine is 1,2,3,4,5,6,7,7,8,9,9,10,10,11,... And I've confirmed it through 8, after writing a program that, unlike my first one, won't take until the heat death of the universe to finish. That suggests a new sequence: The number of unique ways N lattice points can be placed on an N by N grid with distinct mutual distances: Not counting rotations or reflections as distinct, it's 1,2,5,23,35,2,1,0,0,0,... I'd add it, except that I seem to have forgotten my OEIS password. So, there's no way to have 8 points in an 8 by 8 grid. How about 7 points in an 8 by 8 grid? There are 11959 ways. Quite a difference. Anyone want to see them all? I didn't think so. Here's the unique solution for 7 on a 7 by 7 grid: * - * - - - - - - * - - - - - - - - - - * * - - - - - - - - - - - - - - - - - - * - - - - - - - *