%I #20 Feb 16 2025 08:33:30
%S 1,10,101,1010,10101,101011,1010111,10101111,101011111,1010111111,
%T 10101111111,101011111111,1010111111111,10101111111111,
%U 101011111111111,1010111111111111,10101111111111111,101011111111111111,1010111111111111111,10101111111111111111
%N Binary representation of the middle column of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H Robert Price, <a href="/A267879/b267879.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F Conjectures from _Colin Barker_, Jan 22 2016 and Apr 20 2019: (Start)
%F a(n) = 11*a(n-1)-10*a(n-2) for n>4.
%F G.f.: (1-x+x^2-x^3+x^4) / ((1-x)*(1-10*x)).
%F (End)
%F Conjecture: a(n) = (9091*10^(n-3) - 1)/9 for n > 2. - _Stefano Spezia_, Dec 25 2021
%t rule=233; 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 Cf. A267868.
%K nonn,easy,changed
%O 0,2
%A _Robert Price_, Jan 21 2016