A382609 Semiperimeter of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

1, 6, 6, 15, 28, 66, 153, 378, 946, 2415, 6216, 16110, 41905, 109278, 285390, 746031, 1951300, 5105610, 13361865, 34974066, 91550746, 239662671, 627412176, 1642533270, 4300121953, 11257726326, 29472885078, 77160650703, 202008616876, 528864471570, 1384583619321

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, the long leg is A382608(2,2) = 4 and the hypotenuse is A382608(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. A000045, A382608, A382610.

Programs

Mathematica

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

Formula

a(n) = (A382608(n,1) + A382608(n,2) + A382608(n,3))/2.

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