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.

2, 11, 12, 26, 27, 47, 29, 49, 73, 104, 105, 108, 79, 144, 53, 112, 188, 238, 117, 199, 244, 293, 297, 86, 355, 419, 162, 423, 311, 431, 496, 435, 264, 319, 576, 656, 215, 448, 661, 126, 752, 601, 680, 849, 687, 610, 944, 952, 276, 469, 1060, 1166, 174, 797, 979

Offset

1,1

Comments

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 ).

Links

Table of n, a(n) for n=1..55.

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) = floor((3*4/(3+4))^2) = 2.

Crossrefs

Cf. A374597.

Sequence in context: A137001 A136996 A238109 * A113720 A034118 A140148

Adjacent sequences: A374593 A374594 A374595 * A374597 A374598 A374599

Keyword

nonn

Author

Alexander M. Domashenko, Jul 13 2024

Status

approved