A381483 Area of the unique primitive Pythagorean triple whose inradius is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

6, 6, 30, 330, 6090, 153510, 4652340, 158459730, 5854550130, 229936985850, 9477338186316, 406314955623486, 18001068994899900, 820015284879972900, 38258577340819383240, 1822437624604345219170, 88405834606456644170370, 4358080082619077400555090, 217935771356984568896708700

Offset

0,1

References

Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.

Links

Table of n, a(n) for n=0..18.

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

Formula

a(n) = (A383251(n,1) * A383251(n,2))/2.

a(n) = A000108(n)*(A000108(n) + 1)*(2*A000108(n) + 1).

Example

For n=2, the short leg is A382608(2,1) = 3 and the long leg is A382608(2,2) = 4 so the area is then a(2) = (3 * 4 )/2 = 6.

Mathematica

a=Table[(2n)!/(n!(n+1)!), {n, 0, 18}]; Apply[Join, Map[{#(#+1)(2#+1)}&, a]]

Crossrefs

Cf. A000108, A383251, A382114.

Sequence in context: A074002 A359741 A382610 * A140959 A015699 A244416

Adjacent sequences: A381480 A381481 A381482 * A381484 A381485 A381486

Keyword

nonn,easy

Author

Miguel-Ángel Pérez García-Ortega, Apr 22 2025

Status

approved