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 A095122 #27 Aug 02 2025 06:29:57
%S A095122 0,1,1,6,15,45,120,325,861,2278,5995,15753,41328,108345,283881,743590,
%T A095122 1947351,5099221,13351528,34957341,91523685,239618886,627341331,
%U A095122 1642418641,4299936480,11257426225,29472399505,77159865030,202007345631,528862414653,1384580291160
%N A095122 a(n) = Fibonacci(n)*(2*Fibonacci(n)-1).
%C A095122 a(n) mod 2 = Fibonacci(n) mod 2 = A011655(n).
%C A095122 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 is (2*A000045(n)-1, 2*A000045(n)*(A000045(n)-1), 2*A000045(n)*(A000045(n)-1)+1) and its semiperimeter is a(n). - _Miguel-Ángel Pérez García-Ortega_, Apr 13 2025
%D A095122 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A095122 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-5,-1,1).
%F A095122 G.f.: x*(1-2*x+2*x^2+x^3)/((1+x)*(1-x-x^2)*(1-3*x+x^2)).
%F A095122 a(n) = 2*(Fibonacci(2n-1)+Fibonacci(2n+1))/5-Fibonacci(n)+4*(-1)^n/5.
%F A095122 a(n) = 2*Lucas(2n)/5-Fibonacci(n)+4*(-1)^n/5.
%F A095122 a(n) = 2*A000032(2n)/5-A000045(n)+4*(-1)^n/5.
%F A095122 a(n) = 3*a(n-1)+a(n-2)-5*a(n-3)-a(n-4)+a(n-5), with a(0)=0, a(1)=1, a(2)=1, a(3)=6, a(4)=15. - _Harvey P. Dale_, Jan 14 2012
%t A095122 #(2#-1)&/@Fibonacci[Range[0,30]] (* or *) LinearRecurrence[{3,1,-5,-1,1},{0,1,1,6,15},30] (* _Harvey P. Dale_, Jan 14 2012 *)
%Y A095122 Cf. A000032, A000045, A011655, A382843, A382844, A382845.
%K A095122 easy,nonn
%O A095122 0,4
%A A095122 _Paul Barry_, May 29 2004