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A266670 Binary representation of the n-th iteration of the "Rule 53" elementary cellular automaton starting with a single ON (black) cell. 10

%I

%S 1,11,1000,1011111,1000000,11011111111,1000000000,111011111111111,

%T 1000000000000,1111011111111111111,1000000000000000,

%U 11111011111111111111111,1000000000000000000,111111011111111111111111111,1000000000000000000000,1111111011111111111111111111111

%N Binary representation of the n-th iteration of the "Rule 53" 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="/A266670/b266670.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 03 2016 and Apr 16 2019: (Start)

%F a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>5.

%F G.f.: (1+11*x-10001*x^2+890100*x^3+10000*x^4-2000000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)).

%F (End)

%t rule=53; 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. A266669.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 02 2016

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Last modified April 9 20:46 EDT 2020. Contains 333363 sequences. (Running on oeis4.)