A383958 Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000108(n) and its long leg and hypotenuse are consecutive natural numbers.

1, 1, 7, 49, 391, 3527, 34847, 368081, 4089799, 47278087, 564211231, 6911587591, 86537984287, 1103800819999, 14305258627199, 187980039148049, 2500329655657799, 33615543148288199, 456277455475379999, 6246438365457952199, 86175353776521952799, 1197196443787879360799, 16738118900293300099199

Offset

0,3

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) = A383615(n,1) + A383615(n,2).

a(n) = 2*A000108(n)^2 - 1.

a(n) = 2*A001246(n) - 1.

Example

For n=3, the short leg is A383615(3,1) = 3 and the long leg is A383615(3,2) = 4 so the sum of the legs is then a(3) = 3 + 4 = 7.

Mathematica

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

Crossrefs

Cf. A000108, A383615, A131428, A383616, A381846, A001246.

Sequence in context: A366432 A349781 A199554 * A343583 A221462 A374855

Adjacent sequences: A383955 A383956 A383957 * A383959 A383960 A383961

Keyword

nonn,easy

Author

Miguel-Ángel Pérez García-Ortega, May 16 2025

Status

approved