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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 (list; graph; refs; listen; history; text; internal format)
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 Forišek, Sep 06 2011

STATUS

approved

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Last modified December 7 03:44 EST 2022. Contains 358649 sequences. (Running on oeis4.)