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%I #32 Feb 06 2024 19:30:49
%S 0,0,8,80,404,1392,3880,9208,19536,38096,69288,119224,196036,310008,
%T 474336,705328,1023216,1451904,2020232,2762848,3719420,4937200,
%U 6469424,8378184,10734664,13618168,17119288,21338760,26390452,32400592,39508656,47870200,57655752
%N Number of acute triangles on an n X n grid (or geoboard).
%C Place all bounding boxes of A280653 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) * A280653(i,j) where k=1 when i=j and k=2 otherwise. - _Lars Blomberg_, Feb 26 2017
%C According to Langford (p. 243), the leading order is (53/150-Pi/40)*C(n^2,3). See A093072. - _Michael R Peake_, Jan 15 2021
%H Lars Blomberg, <a href="/A190019/b190019.txt">Table of n, a(n) for n = 1..5000</a>
%H Margherita Barile, <a href="http://mathworld.wolfram.com/Geoboard.html">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/AcuteTriangle.html">Acute Triangle</a>.
%F a(n) = A045996(n) - A077435(n) - A190020(n).
%Y Cf. A045996, A077435, A093072, A280653.
%Y Cf. A103429 (analogous problem on a 3-dimensional grid).
%K nonn
%O 1,3
%A _Martin Renner_, May 04 2011
%E Extended by _Ray Chandler_, May 04 2011
%E More terms from _Lars Blomberg_, Feb 26 2017
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