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A266255 Decimal representation of the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell. 2

%I

%S 1,4,3,124,3,2044,3,32764,3,524284,3,8388604,3,134217724,3,2147483644,

%T 3,34359738364,3,549755813884,3,8796093022204,3,140737488355324,3,

%U 2251799813685244,3,36028797018963964,3,576460752303423484,3,9223372036854775804,3

%N Decimal representation of the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell.

%C Rule 43 also generates this sequence.

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

%H Robert Price, <a href="/A266255/b266255.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 <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 27 2015 and Apr 14 2019: (Start)

%F a(n) = (7*(-1)^n+2^(2*n+1)-(-1)^n*2^(2*n+1)-1)/2 for n>0.

%F a(n) = 17*a(n-2)-16*a(n-4) for n>4.

%F G.f.: (1+4*x-14*x^2+56*x^3-32*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).

%F (End)

%t rule=11; 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. A266253, A266254, A266070, A266071, A081253, A266256, A266257, A266258, A266259.

%K nonn,easy

%O 0,2

%A _Robert Price_, Dec 25 2015

%E Conjectures from _Colin Barker_, Apr 14 2019

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Last modified July 11 20:03 EDT 2020. Contains 335652 sequences. (Running on oeis4.)