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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.
(Formerly M1997 N0788)
6

%I M1997 N0788

%S 0,1,2,11,32,50,132,380,368,1135,1120,4348,3622,10568,30634,46304,

%T 55576,152210

%N 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.

%C This means no three on any line, not just lines in the X or Y directions.

%D 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.

%D R. K. Guy, Unsolved combinatorial problems, pp. 121-127 of D. J. A. Welsh, editor, Combinatorial Mathematics and Its Applications. Academic Press, NY, 1971.

%D 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.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Benjamin Chaffin, <a href="http://wso.williams.edu/~bchaffin/no_three_in_line/index.htm">No-Three-In-Line Problem</a>.

%H A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/no3in/readme.html">Progress in the no-three-in-line problem</a>

%H A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/no3in/table_old.txt">Solutions of the no-three-in-line problem</a>

%H A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/no3in/table.txt">Solutions of the no-three-in-line problem</a>

%H M. Gardner, R. L. Graham, M. Meierruth, R. Jacobson, <a href="/A000755/a000755_3.pdf">Correspondence, 1976</a>

%H R. K. Guy and P. A. Kelly, <a href="/A000755/a000755_1.pdf">The No-Three-Line Problem</a>, Research Paper 33, Department of Mathematics, Univ. of Calgary, Calgary, Alberta, 1968. [Annotated scanned copy]

%H R. K. Guy and P. A. Kelly, <a href="/A000755/a000755_2.pdf">The No-Three-Line Problem</a>, condensed version in Canad. Math. Bull. Vol. 11, pp. 527-531, 1968. [Annotated scanned copy]

%H R. K. Guy, P. A. Kelly, N. J. A. Sloane, <a href="/A000755/a000755.pdf">Correspondence, 1968-1971</a>

%e a(3) = 2:

%e X X o ... o X X

%e X o X ... X o X

%e o X X ... X X o

%Y Cf. A000769 (inequivalent solutions).

%K nonn,nice

%O 1,3

%A _N. J. A. Sloane_

%E More terms from the _Achim Flammenkamp_ web site, May 24 2005

%E a(17) and a(18) from _Benjamin Chaffin_, Apr 05 2006

%E Minor edits from _N. J. A. Sloane_, May 25 2010

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)