A383615 Length of the long leg of the unique primitive Pythagorean triple (x,y,z) such that (x-y+z)/2 = A000108(n) and its long leg and hypotenuse are consecutive natural numbers.

4, 40, 364, 3444, 34584, 367224, 4086940, 47268364, 564177640, 6911470020, 86537568264, 1103799334200, 14305253278320, 187980019758360, 2500329584942460, 33615542888998620, 456277454520102600, 6246438361923425820, 86175353763393711960, 1197196443738946826760

Offset

2,1

Links

Table of n, a(n) for n=2..21.

Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas

Formula

a(n) = 2*C(n)*(C(n) - 1) where C(n) = A000108(n).

Example

Triangles begin:
  n=2:      3,     4,     5;
  n=3:      9,    40,    41.
This sequence is column 2.

Crossrefs

Cf. A000108, A131428 (short leg), A383616 (semiperimeter), A381846 (area).

Sequence in context: A279574 A327675 A191681 * A222273 A220366 A220310

Adjacent sequences: A383612 A383613 A383614 * A383616 A383617 A383618

Keyword

nonn,easy

Author

Miguel-Ángel Pérez García-Ortega, May 02 2025

Status

approved