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%I #15 Apr 20 2019 03:34:50
%S 1,111,10111,1100111,101110111,11001100111,1011101110111,
%T 110011001100111,10111011101110111,1100110011001100111,
%U 101110111011101110111,11001100110011001100111,1011101110111011101110111,110011001100110011001100111,10111011101110111011101110111
%N Binary representation of the n-th iteration of the "Rule 214" 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="/A267804/b267804.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) = 10001*a(n-2)-10000*a(n-4) for n>3.
%F G.f.: (1+111*x+110*x^2-10000*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).
%F (End)
%t rule=214; 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 *)
%Y Cf. A071040.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 20 2016
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