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 A267684 #38 Aug 09 2025 09:33:29
%S A267684 1,100,11011,1110111,111101111,11111011111,1111110111111,
%T A267684 111111101111111,11111111011111111,1111111110111111111,
%U A267684 111111111101111111111,11111111111011111111111,1111111111110111111111111,111111111111101111111111111,11111111111111011111111111111
%N A267684 Binary representation of the n-th iteration of the "Rule 203" elementary cellular automaton starting with a single ON (black) cell.
%D A267684 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267684 Robert Price, <a href="/A267684/b267684.txt">Table of n, a(n) for n = 0..1000</a>
%H A267684 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267684 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267684 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267684 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A267684 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A267684 From _Colin Barker_, Jan 19 2016 and Apr 17 2019: (Start)
%F A267684 a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3) for n>4.
%F A267684 G.f.: (1-11*x+1021*x^2-2110*x^3+1000*x^4) / ((1-x)*(1-10*x)*(1-100*x)).
%F A267684 (End)
%F A267684 The above conjectures are correct. Also a(n) = (10*100^n - 9*10^n - 1)/9 for n > 1. - Karl V. Keller, Jr., Jun 07 2022
%t A267684 rule=203; 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 *)
%t A267684 LinearRecurrence[{111, -1110, 1000}, {1, 100, 11011, 1110111, 111101111}, 20] (* _Paolo Xausa_, Aug 07 2025 *)
%o A267684 (Python) print([1, 100]+[(10*100**n - 9*10**n - 1)//9 for n in range(2, 50)]) # Karl V. Keller, Jr., Jun 07 2022
%Y A267684 Cf. A267683, A267685.
%Y A267684 Essentially the same as A138148.
%K A267684 nonn,easy
%O A267684 0,2
%A A267684 _Robert Price_, Jan 19 2016