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A266284 Decimal representation of the n-th iteration of the "Rule 13" elementary cellular automaton starting with a single ON (black) cell. 1

%I

%S 1,2,5,106,21,1962,85,32426,341,522922,1365,8383146,5461,134195882,

%T 21845,2147396266,87381,34359388842,349525,549754415786,1398101,

%U 8796087429802,5592405,140737465985706,22369621,2251799724206762,89478485,36028796661050026,357913941

%N Decimal representation of the n-th iteration of the "Rule 13" 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="/A266284/b266284.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) = 21*a(n-2)-84*a(n-4)+64*a(n-6) for n>5.

%F G.f.: (1+2*x-16*x^2+64*x^3-96*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

%F (End)

%t rule=13; 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. A266282.

%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 February 22 09:22 EST 2020. Contains 332133 sequences. (Running on oeis4.)