cp's OEIS Frontend

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.

%I A000755 M1997 N0788 #39 Jan 13 2023 19:19:55
%S A000755 0,1,2,11,32,50,132,380,368,1135,1120,4348,3622,10568,30634,46304,
%T A000755 55576,152210
%N 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.
%C A000755 This means no three on any line, not just lines in the X or Y directions.
%D A000755 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 A000755 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 A000755 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 A000755 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000755 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000755 Benjamin Chaffin, <a href="http://wso.williams.edu/~bchaffin/no_three_in_line/index.htm">No-Three-In-Line Problem</a>.
%H A000755 A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/no3in/readme.html">Progress in the no-three-in-line problem</a>
%H A000755 A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/no3in/table_old.txt">Solutions of the no-three-in-line problem</a>
%H A000755 A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/no3in/table.txt">Solutions of the no-three-in-line problem</a>
%H A000755 M. Gardner, R. L. Graham, M. Meierruth, R. Jacobson, <a href="/A000755/a000755_3.pdf">Correspondence, 1976</a>
%H A000755 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 A000755 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 A000755 R. K. Guy, P. A. Kelly, N. J. A. Sloane, <a href="/A000755/a000755.pdf">Correspondence, 1968-1971</a>
%e A000755 a(3) = 2:
%e A000755 X X o ... o X X
%e A000755 X o X ... X o X
%e A000755 o X X ... X X o
%Y A000755 Cf. A000769 (inequivalent solutions).
%K A000755 nonn,nice,more
%O A000755 1,3
%A A000755 _N. J. A. Sloane_
%E A000755 More terms from the _Achim Flammenkamp_ web site, May 24 2005
%E A000755 a(17) and a(18) from _Benjamin Chaffin_, Apr 05 2006
%E A000755 Minor edits from _N. J. A. Sloane_, May 25 2010