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%I #17 Apr 17 2019 10:04:05
%S 1,3,7,15,31,63,127,255,510,1021,2042,4085,8170,16341,32682,65365,
%T 130730,261461,522922,1045845,2091690,4183381,8366762,16733525,
%U 33467050,66934101,133868202,267736405,535472810,1070945621,2141891242,4283782485,8567564970
%N Decimal representation of the middle column of the "Rule 111" 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="/A267258/b267258.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 17 2019: (Start)
%F a(n) = (383*2^n-32*((-1)^n+3))/192 for n>5.
%F G.f.: (1+x-x^8) / ((1-x)*(1+x)*(1-2*x)).
%F (End)
%t rule=111; 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. A267253.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 12 2016
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