cp's OEIS Frontend

A267811 Binary representation of the n-th iteration of the "Rule 217" elementary cellular automaton starting with a single ON (black) cell.

%I A267811 #20 Aug 09 2025 10:27:39
%S A267811 1,1,11011,1110111,111101111,11111011111,1111110111111,
%T A267811 111111101111111,11111111011111111,1111111110111111111,
%U A267811 111111111101111111111,11111111111011111111111,1111111111110111111111111,111111111111101111111111111,11111111111111011111111111111
%N A267811 Binary representation of the n-th iteration of the "Rule 217" elementary cellular automaton starting with a single ON (black) cell.
%C A267811 Conjectures from Barker confirmed by later formula. - _Ray Chandler_, Aug 09 2025
%D A267811 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A267811 Robert Price, <a href="/A267811/b267811.txt">Table of n, a(n) for n = 0..1000</a>
%H A267811 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A267811 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A267811 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A267811 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A267811 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A267811 From _Colin Barker_, Jan 22 2016 and Apr 20 2019: (Start)
%F A267811 a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3) for n>4.
%F A267811 G.f.: (1-110*x+12010*x^2-112000*x^3+100000*x^4) / ((1-x)*(1-10*x)*(1-100*x)).
%F A267811 (End)
%F A267811 a(n) = A138148(n) for n > 1. - _Ray Chandler_, Aug 09 2025
%t A267811 rule=217; 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 A267811 Cf. A267810.
%Y A267811 Cf. A138148, A267684.
%K A267811 nonn,easy
%O A267811 0,3
%A A267811 _Robert Price_, Jan 20 2016