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 A033129 #63 Oct 02 2022 18:20:51
%S A033129 0,1,3,6,13,27,54,109,219,438,877,1755,3510,7021,14043,28086,56173,
%T A033129 112347,224694,449389,898779,1797558,3595117,7190235,14380470,
%U A033129 28760941,57521883,115043766,230087533,460175067,920350134,1840700269
%N A033129 Base-2 digits are, in order, the first n terms of the periodic sequence with initial period [1,1,0].
%C A033129 Number of moves to separate a Hanoi Tower into two towers of even resp. odd stones. - _Martin von Gagern_, May 26 2004
%C A033129 From _Reinhard Zumkeller_, Feb 22 2010: (Start)
%C A033129 Terms of A173593 with initial digits '11' in binary representation: a(n) = A173593(2*n-3) for n>0;
%C A033129 for n>0: a(3*n-1) = A083713(n);
%C A033129 a(n+1) - a(n) = abs(A078043(n)). (End)
%H A033129 Harvey P. Dale, <a href="/A033129/b033129.txt">Table of n, a(n) for n = 0..1000</a>
%H A033129 Mohammad Sajjad Hossain, <a href="https://web.archive.org/web/20050827075933/http://online-judge.uva.es/p/v106/10658.html">reArrange</a>.
%H A033129 James Metz, <a href="http://www.jstor.org/stable/10.5951/mathteacher.107.9.0712">Twists on the Tower of Hanoi</a>, Math. Teacher, Vol. 107, No. 9 (2014), 712-715.
%H A033129 <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%H A033129 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1,-2).
%F A033129 From _Paul Barry_, Jan 23 2004: (Start)
%F A033129 Partial sums of abs(A078043).
%F A033129 G.f.: x*(1+x)/((1-x)*(1-2*x)*(1+x+x^2)) = x*(1+x)/(1-2*x-x^3+2*x^4).
%F A033129 a(n) = (6/7)*2^n - (4/21)*cos(2*Pi*n/3) - (2/21)*sqrt(3)*sin(2*Pi*n/3) - 2/3. (End)
%F A033129 a(n) = a(n-3) + 3 * 2^(n-3). - _Martin von Gagern_, May 26 2004
%F A033129 a(n+1) = 2*a(n) + 1 - 0^((a(n)+1) mod 4). - _Reinhard Zumkeller_, Feb 22 2010
%F A033129 a(n) = floor(2^(n+1)*3/7). - _Jean-Marie Madiot_, Oct 05 2012
%F A033129 a(n) = (1/14)*(-9 - 2*(-1)^floor((2n)/3) + (-1)^(floor((2*n + 7)/3) + 1) + 3*2^(n + 2)). - _John M. Campbell_, Dec 26 2016
%t A033129 Table[(1/14)*(-9 - 2*(-1)^Floor[(2 n)/3] + (-1)^(1 + Floor[(1/3)*(7 + 2 n)]) + 3*2^(2 + n)), {n, 0, 100}] (* _John M. Campbell_, Dec 26 2016 *)
%t A033129 Table[FromDigits[PadRight[{},n,{1,1,0}],2],{n,0,40}] (* _Harvey P. Dale_, Oct 02 2022 *)
%o A033129 (PARI) A033129(n)=3<<(n+1)\7 \\ _M. F. Hasler_, Jun 23 2017
%o A033129 (Python) print([(6*2**n//7) for n in range(50)]) # _Karl V. Keller, Jr._, Jul 11 2022
%Y A033129 Cf. A011655 (repeat 0,1,1), A289006 (the same in octal).
%Y A033129 Cf. A057744, A294627 (first differences).
%K A033129 nonn,base,easy
%O A033129 0,3
%A A033129 _Clark Kimberling_