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A267802 Decimal representation of the n-th iteration of the "Rule 213" elementary cellular automaton starting with a single ON (black) cell. 1

%I

%S 1,3,19,115,499,2035,8179,32755,131059,524275,2097139,8388595,

%T 33554419,134217715,536870899,2147483635,8589934579,34359738355,

%U 137438953459,549755813875,2199023255539,8796093022195,35184372088819,140737488355315,562949953421299

%N Decimal representation of the n-th iteration of the "Rule 213" 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="/A267802/b267802.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 21 2016: (Start)

%F a(n) = 5*a(n-1)-4*a(n-2) for n>3.

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

%F (End)

%F Conjecture: a(n) = 2^(2*n+1) - 13 for n>1. - _Colin Barker_, Nov 25 2016

%t rule=213; 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. A267800.

%K nonn

%O 0,2

%A _Robert Price_, Jan 20 2016

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Last modified July 28 23:26 EDT 2021. Contains 346340 sequences. (Running on oeis4.)