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%I #14 Apr 19 2019 07:11:13
%S 1,2,31,34,471,762,7967,8866,120791,194810,2037023,2277026,30918615,
%T 49850618,521532703,582893218,7914997719,12762196218,133512164639,
%U 149219327650,2026242918359,3267120572666,34179103454495,38200175902370,518718173824983
%N Decimal 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="/A267207/b267207.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 +4*x +39*x^2 +104*x^3 +406*x^4 +812*x^5 +1352*x^6 +1120*x^7 +256*x^8 -3584*x^10) / ((1 -x)*(1 +x)*(1 -4*x)*(1 +4*x)*(1 +x^2)*(1 +2*x +4*x^2)*(1 +16*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]],2],{k,1,rows}] (* Decimal Representation of Rows *)
%Y Cf. A243566.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 11 2016
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