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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 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 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 July 17 12:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)