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%I #21 Jun 13 2022 16:46:56
%S 1,10,10100,1101000,111010100,11110101000,1111101010100,
%T 111111010101000,11111110101010100,1111111101010101000,
%U 111111111010101010100,11111111110101010101000,1111111111101010101010100,111111111111010101010101000,11111111111110101010101010100
%N Binary representation of the n-th iteration of the "Rule 197" 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="/A267677/b267677.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) = 110*a(n-1)-999*a(n-2)-110*a(n-3)+1000*a(n-4) for n>5.
%F G.f.: (1-100*x+9999*x^2+100*x^3-9900*x^4-10000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1-100*x)).
%F (End)
%t rule=197; 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. A267676, A267678.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 19 2016
%E Removed an unjustified claim that _Colin Barker_'s conjectures are correct. Removed a program based on a conjecture. - _Michael De Vlieger_, Jun 13 2022
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