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A266299 Binary representation of the n-th iteration of the "Rule 14" elementary cellular automaton starting with a single ON (black) cell. 3

%I

%S 1,110,11000,1100000,110000000,11000000000,1100000000000,

%T 110000000000000,11000000000000000,1100000000000000000,

%U 110000000000000000000,11000000000000000000000,1100000000000000000000000,110000000000000000000000000,11000000000000000000000000000

%N Binary representation of the n-th iteration of the "Rule 14" elementary cellular automaton starting with a single ON (black) cell.

%C Rules 46, 142 and 174 also generate this sequence.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

%H Robert Price, <a href="/A266299/b266299.txt">Table of n, a(n) for n = 0..999</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_, Dec 28 2015 and Apr 14 2019: (Start)

%F a(n) = 11*10^(2*n-1) for n>0.

%F a(n) = 100*a(n-1) for n>1.

%F G.f.: (1+10*x) / (1-100*x).

%F (End)

%t rule=14; 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]]],{k,1,rows}] (* Binary Representation of Rows *)

%Y Cf. A266298.

%K nonn,easy

%O 0,2

%A _Robert Price_, Dec 26 2015

%E Conjectures from _Colin Barker_, Apr 14 2019

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Last modified August 12 12:23 EDT 2020. Contains 336439 sequences. (Running on oeis4.)