A379508 Sum of the legs of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

1, 97, 3361, 114241, 3880897, 131836321, 4478554081, 152139002497, 5168247530881, 175568277047521, 5964153172084897, 202605639573839041, 6882627592338442561, 233806732499933208097, 7942546277405390632801, 269812766699283348307201, 9165691521498228451812097, 311363698964240484013304161

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, Dec 23 2024

Keywords

• nonn
• easy

Examples

			For n=2, the short leg is A377726(2,1) = 13 and the long leg is A377725(2,2) = 84 so the semiperimeter is then a(2) = 13 + 84 = 97.
		

Links

• Miguel-Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, preprint, 2024.

Crossrefs

Cf. A002315, A377016, A377017, A377726, A378965, A378965.

Programs

Mathematica

s[n_]:=s[n]=Module[{ra},ra=((1+Sqrt[2])^(2n+1)-(Sqrt[2]-1)^(2n+1))/2;{2ra^2-1}];sumas={};Do[sumas=Join[semis,FullSimplify[s[n]]],{n,0,17}];sumas

Formula

a(n) = A377726(n,1) + A377726(n,2).