A272651 The no-3-in-line problem: maximal number of points from an n X n square grid so that no three lie on a line.

1, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92

Offset: 1

Author

N. J. A. Sloane, May 10 2016

Keywords

• nonn
• more

Comments

a(47) is the first open case.

It is conjectured that a(n) < 2n for all sufficiently large n.

A000769 has an extensive list of references and links.

Comment from Warren D. Smith, May 10 2015: 2n is a trivial upper bound, because if you pick 2n+1 points, then some three must lie on a horizontal line.

Apart from the offset this may be the same as A103517. - R. J. Mathar, May 13 2016

Links

• A. Flammenkamp, Progress in the no-three-in-line problem
• A. Flammenkamp, Solutions of the no-three-in-line problem

Crossrefs

Cf. A000769.