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A266068 Binary representation of the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell. 2
1, 100, 10, 1111001, 100, 11111110011, 1000, 111111111100111, 10000, 1111111111111001111, 100000, 11111111111111110011111, 1000000, 111111111111111111100111111, 10000000, 1111111111111111111111001111111, 100000000, 11111111111111111111111110011111111 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Rule 35 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

Empirical g.f.: (1+100*x-10001*x^2+109901*x^3+10000*x^4-120000*x^5) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-10*x^2)). - Colin Barker, Dec 21 2015

EXAMPLE

From Michael De Vlieger, Dec 21 2015: (Start)

First 8 rows, replacing leading zeros with ".", the row converted to its binary equivalent at right:

              1                =               1

            1 0 0              =             100

          . . . 1 0            =              10

        1 1 1 1 0 0 1          =         1111001

      . . . . . . 1 0 0        =             100

    1 1 1 1 1 1 1 0 0 1 1      =     11111110011

  . . . . . . . . . 1 0 0 0    =            1000

1 1 1 1 1 1 1 1 1 1 0 0 1 1 1  = 111111111100111

(End)

MATHEMATICA

rule = 3; 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

Sequence in context: A273479 A333399 A069037 * A285648 A084484 A231891

Adjacent sequences:  A266065 A266066 A266067 * A266069 A266070 A266071

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 20 2015

STATUS

approved

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Last modified August 14 07:04 EDT 2020. Contains 336477 sequences. (Running on oeis4.)