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%I #15 Apr 19 2019 10:06:41
%S 0,2,0,5,2,4,3,10,4,7,8,12,7,12,10,15,12,14,13,20,14,17,18,22,17,22,
%T 20,25,22,24,23,30,24,27,28,32,27,32,30,35,32,34,33,40,34,37,38,42,37,
%U 42,40,45,42,44,43,50,44,47,48,52,47,52,50,55,52,54,53
%N Number of OFF (white) cells in 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="/A267213/b267213.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 13 2016 and Apr 19 2019: (Start)
%F a(n) = a(n-3)+a(n-4)-a(n-7) for n>7.
%F G.f.: x*(2+5*x^2+2*x^4-2*x^5+3*x^6) / ((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2)).
%F (End)
%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 *) nbc=Table[Total[catri[[k]]],{k,1,rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]],{k,1,rows}] (* Number of White cells in stage n *)
%Y Cf. A243566.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 11 2016
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