%I #63 Sep 30 2024 02:26:04
%S 2,10,11,23,24,42,28,46,65,93,94,99,75,128,52,104,168,213,112,185,223,
%T 262,269,84,318,373,156,378,290,391,444,398,252,301,515,584,209,417,
%U 591,124,673,555,621,759,632,568,839,852,269,448,949,1038,172,742,895,1051,679,1077
%N a(n) = floor(area) for the area of the largest square that can be inscribed in the n-th Pythagorean triangle, with one side of the square on the hypotenuse of the triangle, for Pythagorean triangles ordered first by increasing perimeter, then by shorter leg.
%C For a triangle with leg lengths x,y, the square has side length x*y*z/(x*y + z^2) and the area rounded down is a(n) = f(x,y,z) = floor((x*y*z/(x*y + z^2))^2) .
%H Alexander M. Domashenko, <a href="https://www.diofant.ru/problem/3957/">Problem 2176. Two squares in a triangle</a> (in Russian).
%e The first Pythagorean triangle is (x,y,z) = (3,4,5) and the rounded area of the square inside it is a(1) = f(3,4,5) = floor((3*4*5/(3*4+5^2))^2) = 2.
%Y Cf. A376608.
%K nonn
%O 1,1
%A _Alexander M. Domashenko_, Jul 13 2024