A380824 Area of the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

30, 6, 84, 180, 840, 3036, 12654, 51330, 214320, 895356, 3767244, 15880200, 67083870, 283656366, 1200287004, 5081015940, 21514542240, 91113336516, 385900503534, 1634538491850, 6923592200280, 29327695892556, 124231206250884, 526244219948880, 2229186359036190, 9442932766091286

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, Feb 04 2025

Keywords

• nonn
• easy

Examples

			For n=2, the short leg is A380821(2,1) = 7 and the long leg is A380821(2,2) = 24 so the area is then a(2) = (7 * 24 )/2 = 84.
		

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. A380821, A380823, A381721, A000032.

Programs

Mathematica

a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{#(#+1)(2#+1)}&,a]]

Formula

a(n) = (A380821(n,1) * A380821(n,2))/2.

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