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A267538 Binary representation of the middle column of the "Rule 143" elementary cellular automaton starting with a single ON (black) cell.

%I A267538 #31 Feb 16 2025 08:33:29
%S A267538 1,11,110,1100,11001,110011,1100111,11001111,110011111,1100111111,
%T A267538 11001111111,110011111111,1100111111111,11001111111111,
%U A267538 110011111111111,1100111111111111,11001111111111111,110011111111111111,1100111111111111111,11001111111111111111
%N A267538 Binary representation of the middle column of the "Rule 143" elementary cellular automaton starting with a single ON (black) cell.
%H A267538 Robert Price, <a href="/A267538/b267538.txt">Table of n, a(n) for n = 0..1000</a>
%H A267538 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267538 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%H A267538 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267538 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A267538 Conjectures from _Colin Barker_, Jan 17 2016 and Apr 20 2019: (Start)
%F A267538 a(n) = 11*a(n-1)-10*a(n-2) for n > 4. [n range correction by _Karl V. Keller, Jr._, Apr 23 2022]
%F A267538 G.f.: (1-x^2+x^4) / ((1-x)*(1-10*x)).
%F A267538 (End)
%F A267538 Conjecture: a(n) = floor(9901*10^n/9000). - _Karl V. Keller, Jr._, Apr 24 2022
%t A267538 rule=143; 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 A267538 Cf. A267533, A267539.
%K A267538 nonn,easy
%O A267538 0,2
%A A267538 _Robert Price_, Jan 16 2016