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 A097134 #42 Sep 08 2022 08:45:14
%S A097134 1,3,9,24,63,165,432,1131,2961,7752,20295,53133,139104,364179,953433,
%T A097134 2496120,6534927,17108661,44791056,117264507,307002465,803742888,
%U A097134 2104226199,5508935709,14422580928,37758807075,98853840297,258802713816
%N A097134 a(n) = 3*Fibonacci(2*n) + 0^n.
%C A097134 Binomial transform of A097133.
%C A097134 Image of 1/(1-3x) under the mapping g(x)->g(x/(1+x^2)). - _Paul Barry_, Jan 16 2005
%H A097134 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1).
%F A097134 G.f.: (1+x^2)/(1-3*x+x^2).
%F A097134 a(n) = 3*a(n-1) - a(n-2) for n > 2.
%F A097134 a(n) = Sum_{k=0..n} binomial(n, k)*(3*Fibonacci(k)+(-1)^k).
%F A097134 a(n) = A097135(2*n).
%F A097134 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k-1,k)*(-1)^k*3^(n-2*k). - _Paul Barry_, Jan 16 2005
%F A097134 a(n) = Fibonacci(n+2)^2 - Fibonacci(n-2)^2. - _Gary Detlefs_, Dec 03 2010
%F A097134 a(n) = Fibonacci(6*n) - 5*Fibonacci(2*n)^3 for n > 0. - _Gary Detlefs_, Oct 18 2011
%F A097134 E.g.f.: 1 + 6*exp(3*x/2)*sinh(sqrt(5)*x/2)/sqrt(5). - _Stefano Spezia_, Aug 19 2019
%o A097134 (Magma) [3*Fibonacci(2*n)+0^n: n in [0..30]]; // _Vincenzo Librandi_, Apr 21 2011
%o A097134 (PARI) a(n)=3*fibonacci(n+n)+0^n \\ _Charles R Greathouse IV_, Oct 18 2011
%Y A097134 Cf. A000045.
%K A097134 nonn,easy
%O A097134 0,2
%A A097134 _Paul Barry_, Jul 26 2004