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%I #27 May 28 2021 20:00:45
%S 0,0,24,236,1148,3932,10760,25392,53576,103824,188104,322852,529116,
%T 835028,1275360,1893496,2742208,3886568,5402448,7381316,9928860,
%U 13168484,17243896,22319864,28579720,36237928,45532720,56732668
%N Number of obtuse triangles on an n X n grid (or geoboard).
%C Place all bounding boxes of A280652 that will fit into the n X n grid in all possible positions, and the proper rectangles in two orientations: a(n) = Sum_{i=1..n} Sum_{j=1..i} k * (n-i+1) * (n-j+1) * A280652(i,j) where k=1 when i=j and k=2 otherwise. - _Lars Blomberg_, Mar 02 2017
%C According to Langford (p. 243), the leading order is (97/150 + Pi/40)*C(n^2,3). See A093072. - _Michael R Peake_, Jan 15 2021
%H Lars Blomberg, <a href="/A190020/b190020.txt">Table of n, a(n) for n = 1..10000</a>
%H Margherita Barile, <a href="http://mathworld.wolfram.com/Geoboard.html">MathWorld -- Geoboard</a>.
%H Eric Langford, <a href="https://www.jstor.org/stable/2688737">A problem in geometric probability</a>, Mathematics Magazine, Nov-Dec, 1970, 237-244.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ObtuseTriangle.html">Obtuse Triangle</a>.
%F a(n) = A045996(n) - A077435(n) - A190019(n).
%Y Cf. A045996, A077435, A093072, A190019, A280652.
%K nonn
%O 1,3
%A _Martin Renner_, May 04 2011
%E Extended by _Ray Chandler_, May 04 2011
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