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A000755
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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)
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6
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0, 1, 2, 11, 32, 50, 132, 380, 368, 1135, 1120, 4348, 3622, 10568, 30634, 46304, 55576, 152210
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OFFSET
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1,3
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COMMENTS
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This means no three on any line, not just lines in the X or Y directions.
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REFERENCES
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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).
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LINKS
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Table of n, a(n) for n=1..18.
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
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EXAMPLE
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a(3) = 2:
X X o ... o X X
X o X ... X o X
o X X ... X X o
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CROSSREFS
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Cf. A000769 (inequivalent solutions).
Sequence in context: A087933 A190259 A190261 * A183460 A033994 A023659
Adjacent sequences: A000752 A000753 A000754 * A000756 A000757 A000758
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KEYWORD
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nonn,nice,more
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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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
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STATUS
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approved
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