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 A249450 #50 Aug 04 2024 05:39:17
%S A249450 -2,-1,1,6,19,53,142,375,985,2582,6763,17709,46366,121391,317809,
%T A249450 832038,2178307,5702885,14930350,39088167,102334153,267914294,
%U A249450 701408731,1836311901,4807526974,12586269023,32951280097,86267571270,225851433715,591286729877
%N A249450 a(n) = Fibonacci(2*n) - 2.
%H A249450 Colin Barker, <a href="/A249450/b249450.txt">Table of n, a(n) for n = 0..1000</a>
%H A249450 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,1).
%F A249450 G.f.: (-2+7*x-3*x^2)/(1-4*x+4*x^2-x^3).
%F A249450 a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3) for n>2.
%F A249450 a(n) = 3*a(n-1) - a(n-2) + 2.
%F A249450 a(n) = (-2-((3-sqrt(5))/2)^n/sqrt(5)+((3+sqrt(5))/2)^n/sqrt(5)). - _Colin Barker_, Nov 03 2016
%F A249450 E.g.f.: 2*exp(3*x/2)*sinh(sqrt(5)*x/2)/sqr(5) - 2*exp(x). - _Stefano Spezia_, Jun 02 2024
%t A249450 Table[Fibonacci[2 n] - 2, {n, 0, 40}] (* or *) CoefficientList[Series[(-2 + 7 x - 3 x^2) / (1 - 4 x + 4 x^2 - x^3), {x, 0, 40}], x]
%t A249450 LinearRecurrence[{4, -4, 1}, {-2, -1, 1}, 30] (* _Robert G. Wilson v_, Dec 19 2014 *)
%o A249450 (Magma) [Fibonacci(2*n)-2: n in [0..40]];
%o A249450 (PARI) Vec((-2+7*x-3*x^2)/(1-4*x+4*x^2-x^3) + O(x^30)) \\ _Colin Barker_, Nov 03 2016
%Y A249450 Cf. A000045, A004146.
%K A249450 sign,easy
%O A249450 0,1
%A A249450 _Vincenzo Librandi_, Dec 15 2014