A382845 Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers.

-1, 1, 1, 7, 17, 49, 127, 337, 881, 2311, 6049, 15841, 41471, 108577, 284257, 744199, 1948337, 5100817, 13354111, 34961521, 91530449, 239629831, 627359041, 1642447297, 4299982847, 11257501249, 29472520897, 77160061447, 202007663441, 528862928881, 1384581123199

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, Apr 06 2025

Keywords

• sign
• easy

Examples

			For n=4, the short leg is A382843(2,1) = 3 and the long leg is A382843(2,2) = 4  so the sum of the legs is then a(4) = 3 + 4 = 7.
		

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, A382843, A382844, A095122, A007598, A080097.

Programs

Mathematica

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

Formula

a(n) = A382843(n,1) + A382843(n,2).

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