A267779 - OEIS

%I #30 Jul 06 2023 13:34:43

%S 1,101,11001,1111101,111111001,11111111101,1111111111001,

%T 111111111111101,11111111111111001,1111111111111111101,

%U 111111111111111111001,11111111111111111111101,1111111111111111111111001,111111111111111111111111101,11111111111111111111111111001

%N Binary representation of the n-th iteration of the "Rule 211" 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="/A267779/b267779.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 20 2016 and Apr 20 2019: (Start)

%F a(n) = 100*a(n-1) + a(n-2) - 100*a(n-3) for n > 3.

%F G.f.: (1 + x + 900*x^2 + 11000*x^3) / ((1-x)*(1+x)*(1-100*x)).

%F (End)

%t rule=211; 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. A267778, A267780.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 20 2016

%E Removed an unjustified claim that _Colin Barker_'s conjectures are correct. - _N. J. A. Sloane_, Jun 13 2022