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 A152732 #25 Sep 08 2022 08:45:39
%S A152732 0,0,2,2,4,10,18,36,74,146,292,586,1170,2340,4682,9362,18724,37450,
%T A152732 74898,149796,299594,599186,1198372,2396746,4793490,9586980,19173962,
%U A152732 38347922,76695844,153391690,306783378,613566756,1227133514,2454267026,4908534052
%N A152732 a(n) + a(n+1) + a(n+2) = 2^n.
%C A152732 0 + 0 + 2 = 2^1; 0 + 2 + 2 = 2^2; 2 + 2 + 4 = 2^3; 2 + 4 + 10 = 2^4; ...
%C A152732 With a(0)=1, a(n) is the number of length n strings in the language over alphabet {0,1} generated by the regular expression: ((0+1)(0*(11)*)*10)*. - _Geoffrey Critzer_, Jan 25 2014
%H A152732 Vincenzo Librandi, <a href="/A152732/b152732.txt">Table of n, a(n) for n = 1..1000</a>
%H A152732 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,2).
%F A152732 From _R. J. Mathar_, Dec 12 2008: (Start)
%F A152732 a(n) = 2*A077947(n-3).
%F A152732 G.f.: 2*x^3/((1-2*x)*(1+x+x^2)). (End)
%F A152732 a(n) = (1/21)*(3*2^n + 18*cos((2*n*Pi)/3) + 2*sqrt(3)*sin((2*n*Pi)/3)). - _Zak Seidov_, Dec 12 2008
%t A152732 k0=k1=0;lst={k0,k1};Do[kt=k1;k1=2^n-k1-k0;k0=kt;AppendTo[lst,k1],{n,1,5!}];lst
%t A152732 LinearRecurrence[{1, 1, 2}, {0, 0, 2}, 70] (* _Vladimir Joseph Stephan Orlovsky_, Feb 24 2012 *)
%o A152732 (PARI) concat([0,0],Vec(2/(1-2*x)/(1+x+x^2)+O(x^99))) \\ _Charles R Greathouse IV_, Feb 24 2012
%o A152732 (Magma) I:=[0,0,2]; [n le 3 select I[n] else Self(n-1) +Self(n-2) +2*Self(n-3): n in [1..30]]; // _G. C. Greubel_, Sep 01 2018
%Y A152732 Cf. A152728, A152729, A152730, A152731, A152725, A152726, A000212.
%K A152732 nonn,easy
%O A152732 1,3
%A A152732 _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008