A265379 Binary representation of the n-th iteration of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell.

1, 111, 11101, 1110011, 111011101, 11100110011, 1110111011101, 111001100110011, 11101110111011101, 1110011001100110011, 111011101110111011101, 11100110011001100110011, 1110111011101110111011101, 111001100110011001100110011, 11101110111011101110111011101

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..499

Eric Weisstein's World of Mathematics, Rule 158

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

Index entries for linear recurrences with constant coefficients, signature (0,10001,0,-10000).

Formula

From Colin Barker, Dec 14 2015 and Apr 18 2019: (Start)

a(n) = 10001*a(n-2) - 10000*a(n-4) for n>3.

G.f.: (1+111*x+1100*x^2-100*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

a(n) = floor((11100 - (n mod 2))*100^n/9999). - Karl V. Keller, Jr., Sep 20 2021

Example

From Michael De Vlieger, Dec 09 2015: (Start)
First 12 rows:
                        1
                      1 1 1
                    1 1 1 0 1
                  1 1 1 0 0 1 1
                1 1 1 0 1 1 1 0 1
              1 1 1 0 0 1 1 0 0 1 1
            1 1 1 0 1 1 1 0 1 1 1 0 1
          1 1 1 0 0 1 1 0 0 1 1 0 0 1 1
        1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1
      1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
    1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1
  1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1
(End)

Mathematica

rule = 158; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}]

Prog

(Python) print([(11100 - (n%2))*100**n//9999 for n in range(30)]) # Karl V. Keller, Jr., Sep 20 2021

Crossrefs

Cf. A071037 (cells), A118171 (decimal).

Sequence in context: A249183 A071033 A267364 * A265688 A138146 A100706

Adjacent sequences: A265376 A265377 A265378 * A265380 A265381 A265382

Keyword

nonn,easy

Author

Robert Price, Dec 07 2015

Status

approved