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 A382844 #12 Apr 13 2025 16:12:15
%S A382844 0,0,0,6,30,180,840,3900,17220,75174,323730,1386264,5909904,25136040,
%T A382844 106739256,452846310,1920088086,8138356716,34486996824,146121685380,
%U A382844 619066205340,2622628707270,11110214972010,47065148576496,199375154768160,844577145104400,3577713520710960
%N A382844 Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000045(n) and its long leg and hypotenuse are consecutive natural numbers.
%D A382844 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A382844 Miguel-Ángel Pérez García-Ortega, <a href="/A382844/a382844.pdf">El Libro de las Ternas Pitagóricas</a>
%F A382844 a(n) = (A382843(n,1) * A382843(n,2))/2.
%F A382844 a(n) = Fibonacci(n)*(Fibonacci(n) - 1)*(2*Fibonacci(n) - 1).
%e A382844 For n=4, the short leg is A382843(2,1) = 3 and the long leg is A382843(2,2) = 4 so the area is then a(4) = (3 * 4)/2 = 6.
%t A382844 a=Table[Fibonacci[n],{n,0,26}];Apply[Join,Map[{#(#-1)(2#-1)}&,a]]
%Y A382844 Cf. A000045, A382843, A382845, A095122.
%K A382844 nonn,easy
%O A382844 0,4
%A A382844 _Miguel-Ángel Pérez García-Ortega_, Apr 06 2025