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 A380824 #20 Mar 14 2025 21:30:53
%S A380824 30,6,84,180,840,3036,12654,51330,214320,895356,3767244,15880200,
%T A380824 67083870,283656366,1200287004,5081015940,21514542240,91113336516,
%U A380824 385900503534,1634538491850,6923592200280,29327695892556,124231206250884,526244219948880,2229186359036190,9442932766091286
%N A380824 Area of the unique primitive Pythagorean triple whose inradius is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%D A380824 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A380824 Miguel-Ángel Pérez García-Ortega, <a href="/A380824/a380824_1.pdf">El Libro de las Ternas Pitagóricas</a>
%F A380824 a(n) = (A380821(n,1) * A380821(n,2))/2.
%F A380824 a(n) = Lucas(n)*(Lucas(n) + 1)*(2*Lucas(n) + 1).
%e A380824 For n=2, the short leg is A380821(2,1) = 7 and the long leg is A380821(2,2) = 24 so the area is then a(2) = (7 * 24 )/2 = 84.
%t A380824 a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{#(#+1)(2#+1)}&,a]]
%Y A380824 Cf. A380821, A380823, A381721, A000032.
%K A380824 nonn,easy
%O A380824 0,1
%A A380824 _Miguel-Ángel Pérez García-Ortega_, Feb 04 2025