cp's OEIS Frontend

A259661 Binary representation of the middle column of the "Rule 54" elementary cellular automaton starting with a single ON (black) cell.

%I A259661 #55 Feb 16 2025 08:33:26
%S A259661 1,11,110,1100,11001,110011,1100110,11001100,110011001,1100110011,
%T A259661 11001100110,110011001100,1100110011001,11001100110011,
%U A259661 110011001100110,1100110011001100,11001100110011001,110011001100110011,1100110011001100110,11001100110011001100
%N A259661 Binary representation of the middle column of the "Rule 54" elementary cellular automaton starting with a single ON (black) cell.
%H A259661 Robert Price, <a href="/A259661/b259661.txt">Table of n, a(n) for n = 0..999</a>
%H A259661 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule54.html">Rule 54</a>
%H A259661 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A259661 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%H A259661 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A259661 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A259661 Conjectures from _Colin Barker_, Dec 08 2015 and Apr 17 2019: (Start)
%F A259661 a(n) = 11*a(n-1) - 11*a(n-2) + 11*a(n-3) - 10*a(n-4) for n>3.
%F A259661 G.f.: 1 / ((1-x)*(1-10*x)*(1+x^2)).
%F A259661 (End)
%e A259661 From _Michael De Vlieger_, Dec 09 2015: (Start)
%e A259661 First 8 rows at left, ignoring "0" outside of range of 1's, the center column values in parentheses, and at right the value of center column cells up to that row:
%e A259661                 (1)                 -> 1
%e A259661               1 (1) 1               -> 11
%e A259661             1 0 (0) 0 1             -> 110
%e A259661           1 1 1 (0) 1 1 1           -> 1100
%e A259661         1 0 0 0 (1) 0 0 0 1         -> 11001
%e A259661       1 1 1 0 1 (1) 1 0 1 1 1       -> 110011
%e A259661     1 0 0 0 1 0 (0) 0 1 0 0 0 1     -> 1100110
%e A259661   1 1 1 0 1 1 1 (0) 1 1 1 0 1 1 1   -> 11001100
%e A259661 1 0 0 0 1 0 0 0 (1) 0 0 0 1 0 0 0 1 -> 110011001
%e A259661 (End)
%t A259661 lim = 20; Take[Last@ Take[#, Ceiling[Length[#]/2]] & /@ CellularAutomaton[54, {{1}, 0}, lim], #] & /@ Range@ lim (* _Michael De Vlieger_, Dec 09 2015 *)
%Y A259661 Cf. A071030, A118109, A118108, A133872, A077854.
%K A259661 nonn,easy
%O A259661 0,2
%A A259661 _Robert Price_, Dec 05 2015