A000755 No-3-in-line problem on n X n grid: total number of ways of placing 2n points on n X n grid so no 3 are in a line. No symmetries are taken into account.
0, 1, 2, 11, 32, 50, 132, 380, 368, 1135, 1120, 4348, 3622, 10568, 30634, 46304, 55576, 152210
Offset: 1
Examples
a(3) = 2: X X o ... o X X X o X ... X o X o X X ... X X o
References
- M. A. Adena, D. A. Holton and P. A. Kelly, Some thoughts on the no-three-in-line problem, pp. 6-17 of Combinatorial Mathematics (Proceedings 2nd Australian Conf.), Lect. Notes Math. 403, 1974.
- R. K. Guy, Unsolved combinatorial problems, pp. 121-127 of D. J. A. Welsh, editor, Combinatorial Mathematics and Its Applications. Academic Press, NY, 1971.
- R. K. Guy and P. A. Kelly, The No-Three-Line Problem. Research Paper 33, Department of Mathematics, Univ. of Calgary, Calgary, Alberta, 1968. Condensed version in Canad. Math. Bull. Vol. 11, pp. 527-531, 1968.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Benjamin Chaffin, No-Three-In-Line Problem.
- A. Flammenkamp, Progress in the no-three-in-line problem
- A. Flammenkamp, Solutions of the no-three-in-line problem
- A. Flammenkamp, Solutions of the no-three-in-line problem
- M. Gardner, R. L. Graham, M. Meierruth, R. Jacobson, Correspondence, 1976
- R. K. Guy and P. A. Kelly, The No-Three-Line Problem, Research Paper 33, Department of Mathematics, Univ. of Calgary, Calgary, Alberta, 1968. [Annotated scanned copy]
- R. K. Guy and P. A. Kelly, The No-Three-Line Problem, condensed version in Canad. Math. Bull. Vol. 11, pp. 527-531, 1968. [Annotated scanned copy]
- R. K. Guy, P. A. Kelly, N. J. A. Sloane, Correspondence, 1968-1971
Crossrefs
Cf. A000769 (inequivalent solutions).
Extensions
More terms from the Achim Flammenkamp web site, May 24 2005
a(17) and a(18) from Benjamin Chaffin, Apr 05 2006
Minor edits from N. J. A. Sloane, May 25 2010
Comments