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Number of acute isosceles triangles on an n X n grid.
4

%I #26 May 28 2021 19:54:06

%S 0,0,8,48,164,448,976,1864,3328,5512,8640,12984,18836,26576,36584,

%T 49056,64560,83640,106904,134816,168004,206952,252480,305360,366312,

%U 436120,515864,605928,707644,822120,950216,1092784,1251784,1427848,1622416,1835968,2070404

%N Number of acute isosceles triangles on an n X n grid.

%C Place all bounding boxes of A279418 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) * A279418(i,j))) where k=1 when i=j and k=2 otherwise. - _Lars Blomberg_, Mar 02 2017

%H Lars Blomberg, <a href="/A190317/b190317.txt">Table of n, a(n) for n = 1..10000</a> (the first 100 terms from Chai Wah Wu)

%F a(n) = A186434(n) - A187452(n) - A190318(n).

%Y Cf. A186434, A187452, A190318, A279418.

%K nonn

%O 1,3

%A _Martin Renner_, May 08 2011

%E a(10)-a(37) from _Nathaniel Johnston_, May 09 2011