A382114 Semiperimeter 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, 15, 66, 435, 3655, 35245, 369370, 4094091, 47292675, 564261621, 6911763951, 86538608325, 1103803048701, 14305266650521, 187980068232586, 2500329761730811, 33615543537222571, 456277456908296101, 6246438370759741771, 86175353796214314061, 1197196443861278161861, 16738118900567747790121, 235379797036403711485951

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, Apr 22 2025

Keywords

• nonn
• easy

Examples

			For n=2, the short leg is A383251(2,1) = 3, the long leg is A383251(2,2) = 4 and the hypotenuse is A383251(2,3) = 5 so the semiperimeter is then a(2) = (3 + 4 + 5)/2 = 6.
		

References

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

Links

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

Crossrefs

Cf. A000108, A383251, A381483.

Programs

Mathematica

a=Table[(2n)!/(n!(n+1)!),{n,0,23}];Apply[Join,Map[{(#+1)(2#+1)}&,a]]

Formula

a(n) = (A383251(n,1) + A383251(n,2) + A383251(n,3))/2.

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