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 A378966 #9 Jul 13 2025 17:36:33
%S A378966 0,546,132840,27132714,5400270960,1070181351954,211922939930520,
%T A378966 41960773653737946,8308058686721274720,1644954930586205575554,
%U A378966 325692811387179035829960,64485533166912548464047114,12767809924078284782564882640,2527961881127459862292727058546,500523684710829430645198931758200
%N A378966 Area 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.
%D A378966 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
%F A378966 a(n) = (A377726(n,1) * A377726(n,2))/2.
%e A378966 For n=2, the short leg is A377726(2,1) = 13 and the long leg so the semiperimeter is then a(2) = (13 * 84)/2 =546.
%t A378966 ar[n_]:=ar[n]= Module[{ra},ra=((1+Sqrt[2])^(2n+1)-(Sqrt[2]-1)^(2n+1))/2;{ra(ra-1)(2ra-1)}];areas={};Do[areas=Join[areas,FullSimplify[ar[n]]],{n,0,16}];areas
%Y A378966 Cf. A002315, A377016, A377017, A377726, A378965.
%K A378966 nonn,easy
%O A378966 0,2
%A A378966 _Miguel-Ángel Pérez García-Ortega_, Dec 12 2024