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A265720 Binary representation of the n-th iteration of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell. 5
1, 0, 100, 1100011, 10000, 11110001111, 1000000, 111111000111111, 100000000, 1111111100011111111, 10000000000, 11111111110001111111111, 1000000000000, 111111111111000111111111111, 100000000000000, 1111111111111100011111111111111, 10000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Rule 33 also generates this sequence.

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

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

FORMULA

Conjectures from Colin Barker, Dec 14 2015 and Apr 16 2019: (Start)

a(n) = 10101*a(n-2) - 1010100*a(n-4) + 1000000*a(n-6) for n > 5.

G.f.: (1-10001*x^2+1100011*x^3+10000*x^4-1210000*x^5) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).

(End)

EXAMPLE

From Michael De Vlieger, Dec 14 2015: (Start)

First 10 rows, replacing leading zeros with ".", the row converted to its binary equivalent at right:

                  1                    =                   1

                . . 0                  =                   0

              . . 1 0 0                =                 100

            1 1 0 0 0 1 1              =             1100011

          . . . . 1 0 0 0 0            =               10000

        1 1 1 1 0 0 0 1 1 1 1          =         11110001111

      . . . . . . 1 0 0 0 0 0 0        =             1000000

    1 1 1 1 1 1 0 0 0 1 1 1 1 1 1      =     111111000111111

  . . . . . . . . 1 0 0 0 0 0 0 0 0    =           100000000

1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1  = 1111111100011111111

(End)

MATHEMATICA

rule = 1; 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. A265718.

Sequence in context: A202055 A185303 A139110 * A343182 A013855 A204576

Adjacent sequences:  A265717 A265718 A265719 * A265721 A265722 A265723

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 14 2015

STATUS

approved

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Last modified July 24 17:43 EDT 2021. Contains 346273 sequences. (Running on oeis4.)