%I #28 Jun 13 2022 16:45:14

%S 1,11,11000,11111,110000000,111111111,1100000000000,1111111111111,

%T 11000000000000000,11111111111111111,110000000000000000000,

%U 111111111111111111111,1100000000000000000000000,1111111111111111111111111,11000000000000000000000000000

%N Binary representation of the n-th iteration of the "Rule 117" 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="/A267273/b267273.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 14 2016 and Apr 19 2019: (Start)

%F a(n) = 10001*a(n-2)-10000*a(n-4) for n>5.

%F G.f.: (1+11*x+999*x^2-98900*x^3-1000*x^4+100000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

%F (End)

%F a(n) = A266983(n), n>1. - _R. J. Mathar_, Jan 17 2016

%t rule=117; 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. A267272, A267274.

%K nonn

%O 0,2

%A _Robert Price_, Jan 12 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