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%I #20 Jun 14 2022 01:27:10
%S 1,0,10101,1100011,111010111,11110001111,1111101011111,
%T 111111000111111,11111110101111111,1111111100011111111,
%U 111111111010111111111,11111111110001111111111,1111111111101011111111111,111111111111000111111111111,11111111111110101111111111111
%N Binary representation of the n-th iteration of the "Rule 201" 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="/A267680/b267680.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 19 2016 and Apr 20 2019: (Start)
%F a(n) = 101*a(n-1)-10100*a(n-3)+10000*a(n-4) for n>4.
%F G.f.: (1-101*x+10101*x^2+89910*x^3-101000*x^4) / ((1-x)*(1-10*x)*(1+10*x)*(1-100*x)).
%F (End)
%t rule=201; 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. A267679, A267681.
%K nonn,easy
%O 0,3
%A _Robert Price_, Jan 19 2016