

A175383


Number of complete quadrangles on an (n X n)grid (or geoplane)


9



0, 1, 78, 1278, 9498, 47331, 175952, 545764, 1461672, 3507553, 7701638, 15773526, 30375194, 55695587, 97777392, 165310348, 270478344, 430196181, 666685134, 1010083690, 1498720098, 2182544223
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OFFSET

1,3


COMMENTS

A complete quadrangle is a set of four points, no three collinear, and the six lines which join them.
Number of ways to arrange 4 indistinguishable points on an n X n square grid so that no three points are collinear at any angle. Column 4 of A194193.  R. H. Hardin, Aug 18 2011


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..55
Weisstein, Eric W.: MathWorld  Complete Quadrangle.


FORMULA

a(n) = A189345(n)  A189346(n)  A178256(n).
a(n) = (1/3)*A189412(n) + A189413(n).


EXAMPLE

From R. H. Hardin, Aug 18 2011 (Start):
Some solutions for 3X3
..0..1..1....1..1..0....1..0..1....0..1..1....0..0..0....1..1..0....1..1..0
..1..0..0....0..0..0....1..0..0....1..1..0....1..1..0....0..0..1....1..0..0
..1..0..0....1..0..1....0..0..1....0..0..0....0..1..1....0..1..0....0..1..0


CROSSREFS

Sequence in context: A128951 A272383 A027786 * A190396 A230521 A264362
Adjacent sequences: A175380 A175381 A175382 * A175384 A175385 A175386


KEYWORD

nonn


AUTHOR

Martin Renner, Apr 19 2011


EXTENSIONS

a(6)  a(22) from Nathaniel Johnston, Apr 25 2011
a(7)  a(22) corrected by Nathaniel Johnston, based on another correction by Michal ForiĊĦek, Sep 06 2011


STATUS

approved



