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 A267777 #26 Feb 16 2025 08:33:29
%S A267777 1,1,11001,1111001,111111001,11111111001,1111111111001,
%T A267777 111111111111001,11111111111111001,1111111111111111001,
%U A267777 111111111111111111001,11111111111111111111001,1111111111111111111111001,111111111111111111111111001,11111111111111111111111111001
%N A267777 Binary representation of the n-th iteration of the "Rule 209" elementary cellular automaton starting with a single ON (black) cell.
%C A267777 Rule 241 also generates this sequence.
%D A267777 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267777 Robert Price, <a href="/A267777/b267777.txt">Table of n, a(n) for n = 0..1000</a>
%H A267777 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267777 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267777 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267777 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A267777 Conjectures from _Colin Barker_, Jan 20 2016 and Apr 20 2019: (Start)
%F A267777 a(n) = 101*a(n-1)-100*a(n-2) for n>2.
%F A267777 G.f.: (1-100*x+11000*x^2) / ((1-x)*(1-100*x)).
%F A267777 (End)
%t A267777 rule=209; 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 *) Table[FromDigits[catri[[k]]],{k,1,rows}] (* Binary Representation of Rows *)
%Y A267777 Cf. A267776, A141722.
%K A267777 nonn,easy
%O A267777 0,3
%A A267777 _Robert Price_, Jan 20 2016
%E A267777 Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _Michael De Vlieger_, Jun 13 2022