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Decimal representation of the middle column of the "Rule 109" elementary cellular automaton starting with a single ON (black) cell.
1

%I #15 Apr 19 2019 09:52:31

%S 1,3,7,14,29,59,118,237,475,950,1901,3803,7606,15213,30427,60854,

%T 121709,243419,486838,973677,1947355,3894710,7789421,15578843,

%U 31157686,62315373,124630747,249261494,498522989,997045979,1994091958,3988183917,7976367835

%N Decimal representation of the middle column 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="/A267210/b267210.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) = 2*a(n-1)+a(n-3)-2*a(n-4) for n>3.

%F G.f.: (1+x+x^2-x^3) / ((1-x)*(1-2*x)*(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 *) mc=Table[catri[[k]][[k]],{k,1,rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc,k],2],{k,1,rows}] (* Binary Representation of Middle Column *)

%Y Cf. A243566.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 11 2016