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%I #16 Apr 20 2019 05:55:49
%S 1,2,5,10,21,43,87,175,351,703,1407,2815,5631,11263,22527,45055,90111,
%T 180223,360447,720895,1441791,2883583,5767167,11534335,23068671,
%U 46137343,92274687,184549375,369098751,738197503,1476395007,2952790015,5905580031,11811160063
%N Decimal 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="/A267880/b267880.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://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) = 3*a(n-1)-2*a(n-2) for n>4.
%F G.f.: (1-x+x^2-x^3+x^4) / ((1-x)*(1-2*x)).
%F (End)
%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],2],{k,1,rows}] (* Binary Representation of Middle Column *)
%Y Cf. A267868.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 21 2016
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