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 A382410 #9 Mar 30 2025 18:13:31
%S A382410 6,0,30,84,546,2310,10710,46284,201066,860700,3676470,15642594,
%T A382410 66461766,282027720,1196023110,5069852964,21485317146,91036824270,
%U A382410 385700191830,1634014069044,6922219243506,29324101445100,124221795865230,526219583239434,2229121859293446,9442763903572560
%N A382410 Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 is A000032(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%D A382410 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A382410 Miguel-Ángel Pérez García-Ortega, <a href="/A382410/a382410.pdf">El Libro de las Ternas Pitagóricas</a>
%H A382410 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (6,-2,-29,16,40,-11,-14,2,1).
%F A382410 a(n) = (A382379(n,1) * A382379(n,2))/2.
%F A382410 a(n) = Lucas(n)*(Lucas(n) - 1)*(2*Lucas(n) - 1).
%e A382410 For n=3, the short leg is A382379(2,1) = 5 and the long leg is A382379(2,2) = 12 so the area is then a(3) = (5 * 12)/2 = 30.
%t A382410 a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{#(#-1)(2#-1)}&,a]]
%Y A382410 Cf. A000032, A382379, A382409.
%K A382410 nonn,easy
%O A382410 0,1
%A A382410 _Miguel-Ángel Pérez García-Ortega_, Mar 24 2025