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 A083694 #21 Oct 29 2022 04:49:23
%S A083694 0,2,4,18,56,202,684,2378,8176,28242,97364,335938,1158696,3997082,
%T A083694 13787644,47560698,164059616,565922722,1952143524,6733900658,
%U A083694 23228518936,80126541162,276395677004,953424059818,3288826504656
%N A083694 a(n) = 2*A002532(n).
%H A083694 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,5).
%F A083694 G.f.: 2*x / (1 - 2*x - 5*x^2).
%F A083694 a(n) = 2*a(n-1) + 5*a(n-2), a(0)=0, a(1)=2.
%F A083694 a(n) = 1 / sqrt(6) * ( (1+sqrt(6))^n - (1-sqrt(6))^n ).
%F A083694 a(n) = 2 * A002533(n-1) + a(n-1).
%t A083694 CoefficientList[Series[2x/(1-2x-5x^2), {x, 0, 25}], x]
%t A083694 LinearRecurrence[{2,5},{0,2},40] (* _Harvey P. Dale_, Nov 03 2011 *)
%t A083694 With[{c=Sqrt[6]}, Simplify/@ Table[((1-c)^n+c (1-c)^n-(1+c)^n+c (1+c)^n)/(5c),{n,30}]] (* _Harvey P. Dale_, Nov 03 2011 *)
%K A083694 easy,nonn
%O A083694 0,2
%A A083694 Mario Catalani (mario.catalani(AT)unito.it), May 03 2003