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 A267705 #22 Feb 16 2025 08:33:29
%S A267705 1,10,10101,1101011,111010111,11110101111,1111101011111,
%T A267705 111111010111111,11111110101111111,1111111101011111111,
%U A267705 111111111010111111111,11111111110101111111111,1111111111101011111111111,111111111111010111111111111,11111111111110101111111111111
%N A267705 Binary representation of the n-th iteration of the "Rule 205" elementary cellular automaton starting with a single ON (black) cell.
%D A267705 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267705 Robert Price, <a href="/A267705/b267705.txt">Table of n, a(n) for n = 0..1000</a>
%H A267705 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267705 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267705 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267705 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A267705 Conjectures from _Colin Barker_, Jan 20 2016 and Apr 20 2019: (Start)
%F A267705 a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3) for n>3.
%F A267705 G.f.: (1-101*x+10101*x^2-10100*x^3) / ((1-x)*(1-10*x)*(1-100*x)).
%F A267705 (End)
%t A267705 rule=205; 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 A267705 Cf. A267704, A188530.
%K A267705 nonn,easy
%O A267705 0,2
%A A267705 _Robert Price_, Jan 19 2016