

A000755


No3inline 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



0, 1, 2, 11, 32, 50, 132, 380, 368, 1135, 1120, 4348, 3622, 10568, 30634, 46304, 55576, 152210
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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 nothreeinline problem, pp. 617 of Combinatorial Mathematics (Proceedings 2nd Australian Conf.), Lect. Notes Math. 403, 1974.
R. K. Guy, Unsolved combinatorial problems, pp. 121127 of D. J. A. Welsh, editor, Combinatorial Mathematics and Its Applications. Academic Press, NY, 1971.
R. K. Guy and P. A. Kelly, The NoThreeLine Problem. Research Paper 33, Department of Mathematics, Univ. of Calgary, Calgary, Alberta, 1968. Condensed version in Canad. Math. Bull. Vol. 11, pp. 527531, 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

Table of n, a(n) for n=1..18.
Benjamin Chaffin, NoThreeInLine Problem.
A. Flammenkamp, Progress in the nothreeinline problem
A. Flammenkamp, Solutions of the nothreeinline problem
A. Flammenkamp, Solutions of the nothreeinline problem
M. Gardner, R. L. Graham, M. Meierruth, R. Jacobson, Correspondence, 1976
R. K. Guy and P. A. Kelly, The NoThreeLine Problem, Research Paper 33, Department of Mathematics, Univ. of Calgary, Calgary, Alberta, 1968. [Annotated scanned copy]
R. K. Guy and P. A. Kelly, The NoThreeLine Problem, condensed version in Canad. Math. Bull. Vol. 11, pp. 527531, 1968. [Annotated scanned copy]
R. K. Guy, P. A. Kelly, N. J. A. Sloane, Correspondence, 19681971


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


EXTENSIONS

More terms from the 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


STATUS

approved



