A037185 Number of ways of placing 2n points on n X n grid so no 3 are in a line (solutions with no symmetry).

0, 0, 0, 0, 3, 4, 11, 40, 41, 132, 122, 524, 407, 1284, 3681, 5683, 6800, 18853, 31967, 117347

Offset

1,5

Links

Table of n, a(n) for n=1..20.

Benjamin Chaffin, No-Three-In-Line Problem.

Achim Flammenkamp, Solutions of the no-three-in-line problem

Achim Flammenkamp, Solutions of the no-three-in-line problem

Achim Flammenkamp, Progress in the no-three-in-line problem, J. Combinat. Theory A 60 (1992), 305-311.

Achim Flammenkamp, Progress in the no-three-in-line problem. II, J. Combin. Theory Ser. A 81 (1998), no. 1, 108-113.

Achim Flammenkamp, Number of Solutions of the No-Three-in-Line-Problem on Small Grids

Mitchell Riley, C++/Cuda program (github)

Crossrefs

Cf. A000769, A000755.

Sequence in context: A042273 A179167 A259845 * A299047 A296256 A351510

Adjacent sequences: A037182 A037183 A037184 * A037186 A037187 A037188

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

a(17) and a(18) from Benjamin Chaffin, Apr 05 2006

a(19) from Mitchell Riley, Feb 02 2026

a(20) from Thomas Prellberg added by David Radcliffe, Jun 19 2026

Status

approved