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 A266720 #37 Feb 16 2025 08:33:28
%S A266720 1,10,101,1011,10110,101101,1011010,10110101,101101010,1011010101,
%T A266720 10110101010,101101010101,1011010101010,10110101010101,
%U A266720 101101010101010,1011010101010101,10110101010101010,101101010101010101,1011010101010101010,10110101010101010101
%N A266720 Binary representation of the middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.
%H A266720 Robert Price, <a href="/A266720/b266720.txt">Table of n, a(n) for n = 0..1000</a>
%H A266720 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266720 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%H A266720 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266720 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A266720 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,1,-10).
%F A266720 From _Colin Barker_, Jan 04 2016 and Apr 18 2019: (Start)
%F A266720 a(n) = (-450*(-1)^n+10009*10^n-550)/9900 for n>1.
%F A266720 a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>4.
%F A266720 G.f.: (1+x^3-x^4) / ((1-x)*(1+x)*(1-10*x)).
%F A266720 (End)
%F A266720 a(n) = floor(10009*10^n/9900). - _Karl V. Keller, Jr._, Oct 17 2021
%t A266720 rule=59; rows=20; ca=CellularAutomaton[rule,{{1},0},rows-1,{All,All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]],{rows-k+1,rows+k-1}],{k,1,rows}]; (* Truncated list of each row *) mc=Table[catri[[k]][[k]],{k,1,rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc,k]],{k,1,rows}] (* Binary Representation of Middle Column *)
%o A266720 (Python) print([10009*10**n//9900 for n in range(50)]) # _Karl V. Keller, Jr._, Oct 18 2021
%Y A266720 Cf. A266716, A266719, A266721.
%K A266720 nonn,easy
%O A266720 0,2
%A A266720 _Robert Price_, Jan 03 2016