A382610 Area of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

0, 6, 6, 30, 84, 330, 1224, 4914, 19866, 82110, 341880, 1433790, 6034320, 25461774, 107592030, 455078910, 1925933100, 8153659170, 34527059160, 146226569946, 619340796690, 2623347596766, 11112097049136, 47070075918390, 199388054716704, 844610917608150, 3577801938273654, 15155740689781854, 64200560537978436

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, Mar 31 2025

Keywords

• nonn
• easy

Examples

			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.
		

References

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

Crossrefs

Cf. A000045, A382608, A382609.

Programs

Mathematica

a=Table[Fibonacci[n],{n,0,28}];Apply[Join,Map[{#(#+1)(2#+1)}&,a]]

Formula

a(n) = (A382608(n,1) * A382608(n,2))/2.

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