%I #17 Apr 20 2019 05:35:26
%S 1,7,23,103,375,1639,6007,26215,96119,419431,1537911,6710887,24606583,
%T 107374183,393705335,1717986919,6299285367,27487790695,100788565879,
%U 439804651111,1612617054071,7036874417767,25801872865143,112589990684263,412829965842295
%N Decimal representation of the n-th iteration of the "Rule 214" 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="/A267805/b267805.txt">Table of n, a(n) for n = 0..1000</a>
%H A. J. Macfarlane, <a href="http://www.damtp.cam.ac.uk/user/ajm/Papers2016/GFsForCAsOfEvenRuleNo.ps">Generating functions for integer sequences defined by the evolution of cellular automata...</a>, Fig. 14.
%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 22 2016 and Apr 20 2019: (Start)
%F a(n) = 17*a(n-2)-16*a(n-4) for n>3.
%F G.f.: (1+7*x+6*x^2-16*x^3) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
%F (End)
%t rule=214; 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. A071040.
%K nonn,easy
%O 0,2
%A _Robert Price_, Jan 20 2016
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