A000755 - OEIS

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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)

0, 1, 2, 11, 32, 50, 132, 380, 368, 1135, 1120, 4348, 3622, 10568, 30634, 46304, 55576, 152210 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,3`
	COMMENTS	`This means no three on any line, not just lines in the X or Y directions.`
	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`
	EXAMPLE	`a(3) = 2:` `X X o ... o X X` `X o X ... X o X` `o X X ... X X o`
	CROSSREFS	`Cf. A000769 (inequivalent solutions).` `Sequence in context: A087933 A190259 A190261 * A183460 A033994 A023659` `Adjacent sequences: A000752 A000753 A000754 * A000756 A000757 A000758`
	KEYWORD	`nonn,nice`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com).`
	EXTENSIONS	`More terms from the Flammenkamp web site, May 24 2005` `a(17) and a(18) from Benjamin Chaffin (chaffin(AT)gmail.com), Apr 05 2006` `Minor edits from N. J. A. Sloane, May 25 2010`

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Last modified February 16 21:13 EST 2012. Contains 205971 sequences.