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

0,1

References

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

Links

Table of n, a(n) for n=0..14.

Formula

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

Example

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.

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

Crossrefs

Cf. A002315, A377025, A378380

Sequence in context: A271637 A249126 A337162 * A281690 A201141 A078927

Adjacent sequences: A378381 A378382 A378383 * A378388 A378389 A378390

Keyword

nonn,easy,new

Author

Miguel-Ángel Pérez García-Ortega, Nov 24 2024

Status

approved