A378386 Area of the unique primitive Pythagorean triple whose inradius is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.

6, 840, 142926, 27475440, 5411913654, 1070576860920, 211936375592766, 41961230070745440, 8308074191463867366, 1644955457291036718120, 325692829279638552084654, 64485533774729467185564240, 12767809944726167559580210326, 2527961881828880059792526682840, 500523684734657069477415103656606

Offset: 0

Author

Miguel-Ángel Pérez García-Ortega, Nov 24 2024

Keywords

• nonn
• easy

Examples

			For n=2, the short leg is A377725(2,1) = 15 and the long leg is A377725(2,2) = 112 so the area is then a(2) = (15 * 112)/2 = 840.
		

References

• 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, A377025, A378380

Programs

Mathematica

d[n_]:=d[n]=Module[{r},r=((1+Sqrt[2])^(2n+1)-(Sqrt[2]-1)^(2n+1))/2;{r(r+1)(2r+1)}];areas={};Do[areas=Join[areas,FullSimplify[d[n]]],{n,0,17}];areas

Formula

a(n) = (A377725(n,1) * A377725(n,2))/2.