A378380 Semiperimeter 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, 120, 3486, 114960, 3885078, 131860680, 4478696046, 152139829920, 5168252353446, 175568305155480, 5964153335910078, 202605640528682160, 6882627597903676086, 233806732532369766120, 7942546277594444747406, 269812766700385236436800, 9165691521504650726475078, 311363698964277915773152440

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..17.

Formula

a(n) = (A377725(n,1) + A377725(n,2) + A377725(n,3))/2.

Example

For n=2, the short leg is A377725(2,1) = 15, the long leg is A377725(2,2) = 112 and the hypotenuse is A377725(2,3) = 113 so the semiperimeter is then a(2) = (15 + 112 + 113)/2 = 120.

Mathematica

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

Crossrefs

Cf. A002315, A377025, A378386

Sequence in context: A185757 A075844 A356506 * A354429 A029697 A248045

Adjacent sequences: A378377 A378378 A378379 * A378381 A378382 A378383

Keyword

nonn,easy

Author

Miguel-Ángel Pérez García-Ortega, Nov 24 2024

Status

approved