A267815 - OEIS

%I #15 Apr 20 2019 05:34:26

%S 1,11,10111,1101111,111011111,11110111111,1111101111111,

%T 111111011111111,11111110111111111,1111111101111111111,

%U 111111111011111111111,11111111110111111111111,1111111111101111111111111,111111111111011111111111111,11111111111110111111111111111

%N Binary representation of the n-th iteration of the "Rule 221" 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="/A267815/b267815.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 22 2016 and Apr 20 2019: (Start)

%F a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3) for n>3.

%F G.f.: (1-100*x+10000*x^2-10000*x^3) / ((1-x)*(1-10*x)*(1-100*x)).

%F (End)

%t rule=221; 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. A267814.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 20 2016