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A175383 Number of complete quadrangles on an (n X n)-grid (or geoplane) 9

%I

%S 0,1,78,1278,9498,47331,175952,545764,1461672,3507553,7701638,

%T 15773526,30375194,55695587,97777392,165310348,270478344,430196181,

%U 666685134,1010083690,1498720098,2182544223

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

%C A complete quadrangle is a set of four points, no three collinear, and the six lines which join them.

%C 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

%H R. H. Hardin, <a href="/A175383/b175383.txt">Table of n, a(n) for n = 1..55</a>

%H Weisstein, Eric W.: <a href="http://mathworld.wolfram.com/CompleteQuadrangle.html">MathWorld -- Complete Quadrangle.</a>

%F a(n) = A189345(n) - A189346(n) - A178256(n).

%F a(n) = (1/3)*A189412(n) + A189413(n).

%e From R. H. Hardin, Aug 18 2011 (Start):

%e Some solutions for 3X3

%e ..0..1..1....1..1..0....1..0..1....0..1..1....0..0..0....1..1..0....1..1..0

%e ..1..0..0....0..0..0....1..0..0....1..1..0....1..1..0....0..0..1....1..0..0

%e ..1..0..0....1..0..1....0..0..1....0..0..0....0..1..1....0..1..0....0..1..0

%K nonn

%O 1,3

%A _Martin Renner_, Apr 19 2011

%E a(6) - a(22) from _Nathaniel Johnston_, Apr 25 2011

%E a(7) - a(22) corrected by _Nathaniel Johnston_, based on another correction by Michal ForiĊĦek, Sep 06 2011

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Last modified November 22 06:26 EST 2019. Contains 329389 sequences. (Running on oeis4.)