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

Author

Miguel-Ángel Pérez García-Ortega, May 16 2025

Keywords

• nonn
• easy

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

Formula

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

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

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