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%I #14 Apr 19 2019 07:10:55
%S 1,2,4,9,19,39,79,159,319,639,1278,2557,5114,10229,20458,40917,81834,
%T 163669,327338,654677,1309354,2618709,5237418,10474837,20949674,
%U 41899349,83798698,167597397,335194794,670389589,1340779178,2681558357,5363116714,10726233429
%N Decimal representation of the middle column of the "Rule 107" 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="/A267157/b267157.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 11 2016 and Apr 19 2019: (Start)
%F a(n) = (-(-1)^n+959*2^(n-7)-3)/6 for n>7.
%F a(n) = 2*a(n-1)+a(n-2)-2*a(n-3) for n>4.
%F G.f.: (1-x^2+x^3+x^4-x^10) / ((1-x)*(1+x)*(1-2*x)).
%F (End)
%t rule=107; 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. A267152.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 11 2016