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 A381483 #13 May 01 2025 21:43:23
%S A381483 6,6,30,330,6090,153510,4652340,158459730,5854550130,229936985850,
%T A381483 9477338186316,406314955623486,18001068994899900,820015284879972900,
%U A381483 38258577340819383240,1822437624604345219170,88405834606456644170370,4358080082619077400555090,217935771356984568896708700
%N A381483 Area of the unique primitive Pythagorean triple whose inradius is A000108(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%D A381483 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A381483 Miguel-Ángel Pérez García-Ortega, <a href="/A381483/a381483.pdf">El Libro de las Ternas Pitagóricas</a>
%F A381483 a(n) = (A383251(n,1) * A383251(n,2))/2.
%F A381483 a(n) = A000108(n)*(A000108(n) + 1)*(2*A000108(n) + 1).
%e A381483 For n=2, the short leg is A382608(2,1) = 3 and the long leg is A382608(2,2) = 4 so the area is then a(2) = (3 * 4 )/2 = 6.
%t A381483 a=Table[(2n)!/(n!(n+1)!),{n,0,18}];Apply[Join,Map[{#(#+1)(2#+1)}&,a]]
%Y A381483 Cf. A000108, A383251, A382114.
%K A381483 nonn,easy
%O A381483 0,1
%A A381483 _Miguel-Ángel Pérez García-Ortega_, Apr 22 2025