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A267926 Decimal representation of the n-th iteration of the "Rule 246" elementary cellular automaton starting with a single ON (black) cell. 1

%I

%S 1,7,23,119,375,1911,6007,30583,96119,489335,1537911,7829367,24606583,

%T 125269879,393705335,2004318071,6299285367,32069089143,100788565879,

%U 513105426295,1612617054071,8209686820727,25801872865143,131354989131639,412829965842295

%N Decimal representation of the n-th iteration of the "Rule 246" 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="/A267926/b267926.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. 16

%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 23 2016 and Apr 20 2019: (Start)

%F a(n) = a(n-1)+16*a(n-2)-16*a(n-3) for n>2.

%F G.f.: (1+6*x) / ((1-x)*(1-4*x)*(1+4*x)).

%F (End)

%F Empirical a(n) = (25*4^n-3*(-4)^n-7)/15. - _Colin Barker_, Nov 25 2016 and Apr 20 2019

%t rule=246; 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. A071041.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 22 2016

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Last modified September 16 08:53 EDT 2019. Contains 327092 sequences. (Running on oeis4.)