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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
3
0, 1, 2, 11, 32, 50, 132, 380, 368, 1135, 1120, 4348, 3622, 10568, 30634, 46304, 55576, 152210 (list; graph; listen)
OFFSET

1,3

COMMENT

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

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

Benjamin Chaffin, No-Three-In-Line Problem.

CROSSREFS

Cf. A000769.

Sequence in context: A106847 A092761 A087933 this_sequence A033994 A023659 A094792

Adjacent sequences: A000752 A000753 A000754 this_sequence 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

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Last modified December 2 11:54 EST 2009. Contains 167921 sequences.


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