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A265379 Binary representation of the n-th iteration of the "Rule 158" elementary cellular automaton starting with a single ON (black) cell. 1
1, 111, 11101, 1110011, 111011101, 11100110011, 1110111011101, 111001100110011, 11101110111011101, 1110011001100110011, 111011101110111011101, 11100110011001100110011, 1110111011101110111011101, 111001100110011001100110011, 11101110111011101110111011101 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

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

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

FORMULA

Conjectures 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)

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}]

CROSSREFS

Cf. A071037.

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

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Last modified August 13 04:54 EDT 2020. Contains 336442 sequences. (Running on oeis4.)