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A266069 Decimal representation of the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell. 1
1, 4, 2, 121, 4, 2035, 8, 32743, 16, 524239, 32, 8388511, 64, 134217535, 128, 2147483263, 256, 34359737599, 512, 549755812351, 1024, 8796093019135, 2048, 140737488349183, 4096, 2251799813672959, 8192, 36028797018939391, 16384, 576460752303374335, 32768 (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

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

FORMULA

Empirical g.f.: (1+4*x-17*x^2+45*x^3+16*x^4-64*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1-2*x^2)). - Colin Barker, Dec 21 2015 and Apr 18 2019

EXAMPLE

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

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

              1                =               1 ->     1

            1 0 0              =             100 ->     4

          . . . 1 0            =              10 ->     2

        1 1 1 1 0 0 1          =         1111001 ->   121

      . . . . . . 1 0 0        =             100 ->     4

    1 1 1 1 1 1 1 0 0 1 1      =     11111110011 ->  2035

  . . . . . . . . . 1 0 0 0    =            1000 ->     8

1 1 1 1 1 1 1 1 1 1 0 0 1 1 1  = 111111111100111 -> 32743

(End)

MATHEMATICA

rule = 3; rows = 30; Table[FromDigits[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]], 2], {k, 1, rows}]

CROSSREFS

Cf. A263428, A266068, A266070, A266071, A081253, A266072, A247375, A266073, A266074.

Sequence in context: A335300 A201228 A010319 * A057167 A096683 A158903

Adjacent sequences:  A266066 A266067 A266068 * A266070 A266071 A266072

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 20 2015

STATUS

approved

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Last modified August 8 23:02 EDT 2020. Contains 336300 sequences. (Running on oeis4.)