[seqfan] no square

hv at crypt.org hv at crypt.org
Mon May 16 22:29:16 CEST 2016


A variant of both A271906 and A227133: Size of the largest subset S of the
points of an n X n square grid such that no four of the points of S form
a square.

For n x n it looks rather simple (for the values I've managed to calculate):
  1 3 6 10 15

.. but the full m x n results are not in OEIS, and may hint at more
complexity:

 1  2  3  4  5  6  7  8
 2  3  5  6  8  9 11 12
 3  5  6  8 10 12 14 16
 4  6  8 10 13 15 18 20
 5  8 10 13 15 19
 6  9 12 15 19
 7 11 14 18
 8 12 16 20

I need to rewrite my code to get more results, I want to get at least
up to 8 x 8.

More generally, should all sequences relating to "an n x n grid" be under
consideration for extending to "an m x n grid"? I appreciate a few will
make no sense, but it seems like in most cases it should be a natural
extension - I was surprised not to see it for the recently discussed
right-triangles case.

Hugo


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