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%I #38 Feb 07 2024 01:20:42
%S 0,1,70,1038,7398,35727,130768,400116,1062016,2531001,5529310,
%T 11272710,21639022,39559591,69283632,116910052,190977408,303286461,
%U 469431366,710400658,1053055398,1532253131,2192246528,3088876728,4290532688,5882825641,7969711934,10677299074,14156978846,18591603883,24195121104
%N Number of convex quadrilaterals on an n X n grid (or geoboard).
%C If four points are chosen at random from an n X n grid, the probability that they form a convex quadrilateral approaches 25/36 as n increases, by Sylvester's Four-Point Theorem (see the link). Thanks to _Ed Pegg Jr_ for this comment. - _N. J. A. Sloane_, Jun 15 2020
%H Tom Duff, <a href="/A189413/b189413.txt">Table of n, a(n) for n = 1..192</a>
%H Tom Duff, <a href="/A334708/a334708_3.txt">Data for tables A334708, A334709, A334710, A334711 for grids of size up to 192 X 192</a>.
%H Nathaniel Johnston, <a href="/A189413/a189413.c.txt">C program for computing terms</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConvexPolygon.html">Convex Polygon</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Quadrilateral.html">Quadrilateral</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SylvestersFour-PointProblem.html">Sylvester's Four-Point Problem</a>.
%Y Cf. A175383, A178256, A181944, A189345, A189412, A189414.
%Y This is the main diagonal of A334711.
%K nonn
%O 1,3
%A _Martin Renner_, Apr 21 2011
%E a(6) - a(22) from _Nathaniel Johnston_, Apr 25 2011
%E Terms beyond a(22) from Tom Duff. - _N. J. A. Sloane_, Jun 23 2020
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