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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
Eric Weisstein's World of Mathematics, 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 3 X 3:
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
(End)
CROSSREFS
Sequence in context: A370209 A272383 A027786 * A190396 A230521 A264362
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 July 17 12:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)