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 A382610 #6 Apr 06 2025 14:48:58
%S A382610 0,6,6,30,84,330,1224,4914,19866,82110,341880,1433790,6034320,
%T A382610 25461774,107592030,455078910,1925933100,8153659170,34527059160,
%U A382610 146226569946,619340796690,2623347596766,11112097049136,47070075918390,199388054716704,844610917608150,3577801938273654,15155740689781854,64200560537978436
%N A382610 Area of the unique primitive Pythagorean triple whose inradius is A000045(n) and such that its long leg and its hypotenuse are consecutive natural numbers.
%D A382610 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%F A382610 a(n) = (A382608(n,1) * A382608(n,2))/2.
%F A382610 a(n) = Fibonacci(n)*(Fibonacci(n) + 1)*(2*Fibonacci(n) + 1).
%e A382610 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 A382610 a=Table[Fibonacci[n],{n,0,28}];Apply[Join,Map[{#(#+1)(2#+1)}&,a]]
%Y A382610 Cf. A000045, A382608, A382609.
%K A382610 nonn,easy
%O A382610 0,2
%A A382610 _Miguel-Ángel Pérez García-Ortega_, Mar 31 2025