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

1, 11, 110, 1100, 11001, 110011, 1100110, 11001100, 110011001, 1100110011, 11001100110, 110011001100, 1100110011001, 11001100110011, 110011001100110, 1100110011001100, 11001100110011001, 110011001100110011, 1100110011001100110, 11001100110011001100

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..999

Eric Weisstein's World of Mathematics, Rule 54

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Dec 08 2015 and Apr 17 2019: (Start)

a(n) = 11*a(n-1) - 11*a(n-2) + 11*a(n-3) - 10*a(n-4) for n>3.

G.f.: 1 / ((1-x)*(1-10*x)*(1+x^2)).

(End)

Example

From Michael De Vlieger, Dec 09 2015: (Start)
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:
                (1)                 -> 1
              1 (1) 1               -> 11
            1 0 (0) 0 1             -> 110
          1 1 1 (0) 1 1 1           -> 1100
        1 0 0 0 (1) 0 0 0 1         -> 11001
      1 1 1 0 1 (1) 1 0 1 1 1       -> 110011
    1 0 0 0 1 0 (0) 0 1 0 0 0 1     -> 1100110
  1 1 1 0 1 1 1 (0) 1 1 1 0 1 1 1   -> 11001100
1 0 0 0 1 0 0 0 (1) 0 0 0 1 0 0 0 1 -> 110011001
(End)

Mathematica

lim = 20; Take[Last@ Take[#, Ceiling[Length[#]/2]] & /@ CellularAutomaton[54, {{1}, 0}, lim], #] & /@ Range@ lim (* Michael De Vlieger, Dec 09 2015 *)

Crossrefs

Cf. A071030, A118109, A118108, A133872, A077854.

Sequence in context: A170644 A170692 A278664 * A265699 A267538 A278819

Adjacent sequences: A259658 A259659 A259660 * A259662 A259663 A259664

Keyword

nonn,easy

Author

Robert Price, Dec 05 2015

Status

approved