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 A382409 #11 Mar 30 2025 18:13:07
%S A382409 6,1,15,28,91,231,630,1653,4371,11476,30135,79003,207046,542361,
%T A382409 1420455,3719628,9739491,25500511,66764790,174798253,457637131,
%U A382409 1198124676,3136755615,8212172403,21499810566,56287338481,147362333055,385799868028,1010037606571,2644313494551,6922903755510
%N A382409 Semiperimeter 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 A382409 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A382409 Miguel-Ángel Pérez García-Ortega, <a href="/A382409/a382409.pdf">El Libro de las Ternas Pitagóricas</a>
%H A382409 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-5,-1,1).
%F A382409 a(n) = (A382379(n,1) + A382379(n,2) + A382379(n,3))/2.
%F A382409 a(n) = Lucas(n)*(2*Lucas(n) - 1).
%e A382409 For n=3, the short leg is A382379(2,1) = 5, the long leg is A382379(2,2) = 12 and the hypotenuse is A382379(2,3) = 13 so the semiperimeter is then a(3) = (5 + 12 + 13)/2 = 15.
%t A382409 a=Table[LucasL[n],{n,0,30}];Apply[Join,Map[{#(2#-1)}&,a]]
%Y A382409 Cf. A000032, A382379, A382410.
%K A382409 nonn,easy
%O A382409 0,1
%A A382409 _Miguel-Ángel Pérez García-Ortega_, Mar 24 2025