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Binary representation of the n-th iteration of the "Rule 118" elementary cellular automaton starting with a single ON (black) cell.
1

%I #16 Apr 19 2019 11:23:02

%S 1,111,10011,1111011,100011011,11101011011,1001111011011,

%T 111100011011011,10001101011011011,1110101111011011011,

%U 100111100011011011011,11110001101011011011011,1000110101111011011011011,111010111100011011011011011,10011110001101011011011011011

%N Binary representation of the n-th iteration of the "Rule 118" 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="/A267275/b267275.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 Empirical g.f.: (1 +110*x +9900*x^2 +1100000*x^3 -1210000*x^4 -8900000*x^5 -1091000000*x^6) / ((1 -x)*(1 -10*x)*(1 -100*x)*(1 +100*x)*(1 +10*x +100*x^2)*(1 +10000*x^2)). - _Colin Barker_, Jan 14 2016 and Apr 19 2019

%t rule=118; 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. A071034.

%K nonn

%O 0,2

%A _Robert Price_, Jan 12 2016