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 A266612 #35 Feb 16 2025 08:33:28
%S A266612 1,10,101,1010,10100,101001,1010010,10100101,101001010,1010010101,
%T A266612 10100101010,101001010101,1010010101010,10100101010101,
%U A266612 101001010101010,1010010101010101,10100101010101010,101001010101010101,1010010101010101010,10100101010101010101
%N A266612 Binary representation of the middle column of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.
%H A266612 Robert Price, <a href="/A266612/b266612.txt">Table of n, a(n) for n = 0..1000</a>
%H A266612 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266612 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%H A266612 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266612 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A266612 Conjectures from _Colin Barker_, Jan 02 2016 and Apr 17 2019: (Start)
%F A266612 a(n) = (-9*(-1)^n+99991*2^(n-2)*5^(n-3)-11)/198 for n>2.
%F A266612 a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>2.
%F A266612 G.f.: (1-x^4+x^5) / ((1-x)*(1+x)*(1-10*x)).
%F A266612 (End)
%t A266612 rule=41; 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 *)
%Y A266612 Cf. A266608, A266611, A266613.
%K A266612 nonn,easy
%O A266612 0,2
%A A266612 _Robert Price_, Jan 01 2016
%E A266612 Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _N. J. A. Sloane_, Jun 13 2022