A383957 Sum of the legs of the unique primitive Pythagorean triple whose inradius is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

7, 7, 17, 71, 449, 3697, 35377, 369799, 4095521, 47297537, 564278417, 6911822737, 86538816337, 1103803791601, 14305269324961, 187980077927431, 2500329797088481, 33615543666867361, 456277457385934801, 6246438372527004961, 86175353802778434481, 1197196443885744428881, 16738118900659230353761

Offset

0,1

Links

Table of n, a(n) for n=0..22.

José Miguel Blanco Casado and Miguel-Ángel Pérez García-Ortega, El Libro de las Ternas Pitagóricas

Formula

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

a(n) = 2*(A000108(n))^2 + 4*A000108(n) + 1.

Example

For n=1, the short leg is A383251(1,1) = 3 and the long leg is A383251(1,2) = 4 so the sum of the legs is then a(1) = 3 + 4 = 7.

Mathematica

a=Table[(2n)!/(n!(n+1)!), {n, 0, 23}]; Apply[Join, Map[{2#^2+4#+1}&, a]]

Crossrefs

Cf. A000108, A383251, A381483, A382114, A006007, A058919, A336535.

Sequence in context: A165138 A196395 A382308 * A358380 A139126 A070919

Adjacent sequences: A383954 A383955 A383956 * A383958 A383959 A383960

Keyword

nonn,easy

Author

Miguel-Ángel Pérez García-Ortega, May 16 2025

Status

approved