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

1,1

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) .

Links

Table of n, a(n) for n=1..58.

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

Example

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.

Crossrefs

Cf. A376608.

Sequence in context: A174569 A179884 A174570 * A072545 A023151 A342535

Adjacent sequences: A374594 A374595 A374596 * A374598 A374599 A374600

Keyword

nonn

Author

Alexander M. Domashenko, Jul 13 2024

Status

approved