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 A383833 #13 Jul 13 2025 17:21:48
%S A383833 0,6,84,546,2310,7440,19866,46284,97236,188370,341880,588126,967434,
%T A383833 1532076,2348430,3499320,5086536,7233534,10088316,13826490,18654510,
%U A383833 24813096,32580834,42277956,54270300,68973450,86857056,108449334,134341746,165193860,201738390
%N A383833 Area of the unique primitive Pythagorean triple whose inradius is A000217(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%D A383833 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A383833 Miguel-Ángel Pérez García-Ortega, <a href="/A383833/a383833.pdf">El Libro de las Ternas Pitagóricas</a>
%F A383833 a(n) = A000217(n) * (A000217(n) + 1) * (2*A000217(n) + 1).
%e A383833 For n=1, the short leg is A002061(1) = 3 and the long leg is A212135(2) = 4 so the area is then a(1) = (3 * 4 )/2 = 6.
%t A383833 a=Table[(n(n+1))/2,{n,0,30}];Apply[Join,Map[{#(#+1)(2#+1)}&,a]]
%Y A383833 Cf. A000217, A002061, A058919, A383834, A336535.
%K A383833 nonn,easy
%O A383833 0,2
%A A383833 _Miguel-Ángel Pérez García-Ortega_, May 11 2025