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Binary representation of the n-th iteration of the "Rule 199" elementary cellular automaton starting with a single ON (black) cell.
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%I #23 Jun 14 2022 01:25:09

%S 1,110,11100,1111010,111110100,11111101010,1111111010100,

%T 111111110101010,11111111101010100,1111111111010101010,

%U 111111111110101010100,11111111111101010101010,1111111111111010101010100,111111111111110101010101010,11111111111111101010101010100

%N Binary representation of the n-th iteration of the "Rule 199" 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="/A267688/b267688.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 19 2016: (Start)

%F a(n) = 110*a(n-1) - 999*a(n-2) - 110*a(n-3) + 1000*a(n-4) for n > 4.

%F G.f.: (1 - x^2 + 10*x^3 - 1000*x^4) / ((1-x)*(1+x)*(1-10*x)*(1-100*x)).

%F (End)

%t rule=199; 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. A267687, A267689.

%K nonn

%O 0,2

%A _Robert Price_, Jan 19 2016