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 A377726 #17 Jul 14 2025 22:17:02
%S A377726 84,3280,113764,3878112,131820084,4478459440,152138450884,
%T A377726 5168244315840,175568258308884,5964153062868112,202605638937276964,
%U A377726 6882627588628286880,233806732478308836084,7942546277279354556400,269812766698548756220804,9165691521493946935370112
%N A377726 Lengths of the long leg of the unique primitive Pythagorean triple (x,y,z) such that (x-y+z)/2 is A002315(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%D A377726 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2024.
%F A377726 a(n) = 2 * A002315(n) * (A002315(n) - 1).
%e A377726 Triangles begins:
%e A377726 n=1: 13, 84, 85;
%e A377726 n=2: 81, 3280, 3281;
%e A377726 n=3: 477, 113764, 113765;
%e A377726 ...
%e A377726 This sequence gives the middle column.
%t A377726 ra[n_]:=ra[n]=Module[{ra},ra=((1+Sqrt[2])^(2n+1)-(Sqrt[2]-1)^(2n+1))/2;{2ra-1,2ra^2-2ra,2ra^2-2ra+1}];exradio={};Do[exradio=Join[exradio,FullSimplify[ra[n]]],{n,0,10}];exradio
%Y A377726 Cf. A002315, A377016, A377017, A377725, A362545 (short legs).
%K A377726 nonn,easy
%O A377726 1,1
%A A377726 _Miguel-Ángel Pérez García-Ortega_, Nov 05 2024