This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A189413 #39 Feb 16 2025 08:33:14 %S A189413 0,1,70,1038,7398,35727,130768,400116,1062016,2531001,5529310, %T A189413 11272710,21639022,39559591,69283632,116910052,190977408,303286461, %U A189413 469431366,710400658,1053055398,1532253131,2192246528,3088876728,4290532688,5882825641,7969711934,10677299074,14156978846,18591603883,24195121104 %N A189413 Number of convex quadrilaterals on an n X n grid (or geoboard). %C A189413 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 A189413 Tom Duff, <a href="/A189413/b189413.txt">Table of n, a(n) for n = 1..192</a> %H A189413 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 A189413 Nathaniel Johnston, <a href="/A189413/a189413.c.txt">C program for computing terms</a>. %H A189413 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConvexPolygon.html">Convex Polygon</a>. %H A189413 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Quadrilateral.html">Quadrilateral</a>. %H A189413 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SylvestersFour-PointProblem.html">Sylvester's Four-Point Problem</a>. %Y A189413 Cf. A175383, A178256, A181944, A189345, A189412, A189414. %Y A189413 This is the main diagonal of A334711. %K A189413 nonn %O A189413 1,3 %A A189413 _Martin Renner_, Apr 21 2011 %E A189413 a(6) - a(22) from _Nathaniel Johnston_, Apr 25 2011 %E A189413 Terms beyond a(22) from Tom Duff. - _N. J. A. Sloane_, Jun 23 2020