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 A163305 #15 Mar 08 2021 11:44:26
%S A163305 0,5,10,40,120,400,1280,4160,13440,43520,140800,455680,1474560,
%T A163305 4771840,15441920,49971200,161710080,523304960,1693450240,5480120320,
%U A163305 17734041600,57388564480,185713295360,600980848640,1944814878720
%N A163305 Numerators of fractions in the approximation of the square root of 5 satisfying: a(n)= (a(n-1)+ c)/(a(n-1)+1); with c=5 and a(1)=0. Also product of the powers of two and five times the Fibonacci numbers.
%C A163305 For denominators see: A084057 (= product of Lucas numbers (excluding first number (2)), and powers of 2).
%H A163305 G. C. Greubel, <a href="/A163305/b163305.txt">Table of n, a(n) for n = 1..1000</a>
%H A163305 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,4).
%F A163305 From _Colin Barker_, Jun 20 2012: (Start)
%F A163305 a(n) = 2*a(n-1) + 4*a(n-2).
%F A163305 G.f.: 5*x^2/(1-2*x-4*x^2). (End)
%F A163305 a(n) = 5*A063727(n-1). - _R. J. Mathar_, Mar 08 2021
%t A163305 LinearRecurrence[{2,4},{0,5},30] (* _Harvey P. Dale_, Mar 01 2016 *)
%o A163305 (PARI) a(n)=5*fibonacci(n-1)*2^(n-2) \\ _Franklin T. Adams-Watters_, Aug 06 2009
%Y A163305 Cf. A000032, A000079, A084057, A000045.
%K A163305 nonn,easy
%O A163305 1,2
%A A163305 _Mark Dols_, Jul 24 2009
%E A163305 More terms from _Franklin T. Adams-Watters_, Aug 06 2009