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A374596 Floor(area) for the area of the largest square which fits in each Pythagorean triangle, with sides of the square on the legs of the triangle, for Pythagorean triangles ordered first by increasing perimeter, then shorter leg, then longer leg.

%I A374596 #16 Aug 03 2024 11:58:25
%S A374596 2,11,12,26,27,47,29,49,73,104,105,108,79,144,53,112,188,238,117,199,
%T A374596 244,293,297,86,355,419,162,423,311,431,496,435,264,319,576,656,215,
%U A374596 448,661,126,752,601,680,849,687,610,944,952,276,469,1060,1166,174,797,979
%N A374596 Floor(area) for the area of the largest square which fits in each Pythagorean triangle, with sides of the square on the legs of the triangle, for Pythagorean triangles ordered first by increasing perimeter, then shorter leg, then longer leg.
%C A374596 For a triangle with leg lengths x,y, the square has side length x*y/(x+y) and the area rounded down is a(n) = f(x,y) = floor( (x*y/(x+y))^2 ).
%e A374596 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) = floor((3*4/(3+4))^2) = 2.
%Y A374596 Cf. A374597.
%K A374596 nonn
%O A374596 1,1
%A A374596 _Alexander M. Domashenko_, Jul 13 2024