A374597 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.

2, 10, 11, 23, 24, 42, 28, 46, 65, 93, 94, 99, 75, 128, 52, 104, 168, 213, 112, 185, 223, 262, 269, 84, 318, 373, 156, 378, 290, 391, 444, 398, 252, 301, 515, 584, 209, 417, 591, 124, 673, 555, 621, 759, 632, 568, 839, 852, 269, 448, 949, 1038, 172, 742, 895, 1051, 679, 1077

Offset: 1

Author

Alexander M. Domashenko, Jul 13 2024

Keywords

• nonn

Comments

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) .

Examples

			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.
		

Links

• Alexander M. Domashenko, Problem 2176. Two squares in a triangle (in Russian).

Crossrefs

Cf. A376608.