This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378386 #6 Dec 11 2024 19:21:47
%S A378386 6,840,142926,27475440,5411913654,1070576860920,211936375592766,
%T A378386 41961230070745440,8308074191463867366,1644955457291036718120,
%U A378386 325692829279638552084654,64485533774729467185564240,12767809944726167559580210326,2527961881828880059792526682840,500523684734657069477415103656606
%N 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.
%D A378386 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
%F A378386 a(n) = (A377725(n,1) * A377725(n,2))/2.
%e A378386 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.
%t A378386 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
%Y A378386 Cf. A002315, A377025, A378380
%K A378386 nonn,easy
%O A378386 0,1
%A A378386 _Miguel-Ángel Pérez García-Ortega_, Nov 24 2024