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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
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved