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 A076736 #34 Jan 11 2025 05:20:42
%S A076736 1,1,1,2,1,4,2,8,4,16,8,32,16,64,32,128,64,256,128,512,256,1024,512,
%T A076736 2048,1024,4096,2048,8192,4096,16384,8192,32768,16384,65536,32768,
%U A076736 131072,65536,262144,131072,524288,262144,1048576,524288,2097152
%N A076736 Let u(1) = u(2) = u(3) = 2, u(n) = (1 + u(n-1)*u(n-2))/u(n-3); then a(n) is the denominator of u(n).
%C A076736 The sequence 1,4,2,8,4,... has g.f. (1+4*x)/(1-2*x^2) and a(n) = 2^(n/2)*(1+2*sqrt(2) + (1-2*sqrt(2))*(-1)^n)/2. - _Paul Barry_, Apr 26 2004
%C A076736 The sequence 2,1,4,2,8,... has a(n) = 2^(n/2)*(1+2*sqrt(2)-(1-2*sqrt(2))*(-1)^n)/(2*sqrt(2)) and is essentially the pair-reversal of A016116. - _Paul Barry_, Apr 26 2004
%H A076736 Harvey P. Dale, <a href="/A076736/b076736.txt">Table of n, a(n) for n = 1..1000</a>
%H A076736 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F A076736 For n > 4, a(n) = 2^A028242(n-4).
%F A076736 From _Colin Barker_, Oct 14 2014: (Start)
%F A076736 For n > 5, a(n) = 2*a(n-2).
%F A076736 G.f.: x*(x-1)*(x^3+x^2+2*x+1) / (2*x^2-1). (End)
%t A076736 LinearRecurrence[{0,2},{1,1,1,2,1},50] (* _Harvey P. Dale_, Aug 25 2015 *)
%Y A076736 Cf. A005246, A076737.
%K A076736 frac,nonn,easy
%O A076736 1,4
%A A076736 _Benoit Cloitre_, Nov 24 2002
%E A076736 More terms from _Paul Barry_, Apr 26 2004