%I #15 Apr 19 2019 07:11:23
%S 1,10,11111,100010,111010111,1011111010,1111100011111,10001010100010,
%T 11101011111010111,101111100011111010,111110001010100011111,
%U 1000101011111010100010,1110101111100011111010111,10111110001010100011111010,11111000101011111010100011111
%N Binary representation of the n-th iteration of the "Rule 109" 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="/A267206/b267206.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 +20*x +11311*x^2 +212120*x^3 +13121310*x^4 +131213100*x^5 +1212121000*x^6 +1121100000*x^7 +100000000*x^8 -111000000000*x^10) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 +x^2)*(1 +10*x +100*x^2)*(1 +10000*x^2)). - _Colin Barker_, Jan 13 2016 and Apr 19 2019
%t rule=109; 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. A243566.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 11 2016
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