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 A382609 #7 Apr 06 2025 14:48:50
%S A382609 1,6,6,15,28,66,153,378,946,2415,6216,16110,41905,109278,285390,
%T A382609 746031,1951300,5105610,13361865,34974066,91550746,239662671,
%U A382609 627412176,1642533270,4300121953,11257726326,29472885078,77160650703,202008616876,528864471570,1384583619321
%N A382609 Semiperimeter 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 A382609 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A382609 Miguel-Ángel Pérez García-Ortega, <a href="/A382609/a382609.pdf">El Libro de las Ternas Pitagóricas</a>
%F A382609 a(n) = (A382608(n,1) + A382608(n,2) + A382608(n,3))/2.
%F A382609 a(n) = (Fibonacci(n) + 1)*(2*Fibonacci(n) + 1).
%e A382609 For n=2, the short leg is A382608(2,1) = 3, the long leg is A382608(2,2) = 4 and the hypotenuse is A382608(2,3) = 5 so the semiperimeter is then a(2) = (3 + 4 + 5)/2 = 6.
%t A382609 a=Table[Fibonacci[n],{n,0,30}];Apply[Join,Map[{(#+1)(2#+1)}&,a]]
%Y A382609 Cf. A000045, A382608, A382610.
%K A382609 nonn,easy
%O A382609 0,2
%A A382609 _Miguel-Ángel Pérez García-Ortega_, Mar 31 2025