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A265721 Decimal representation of the n-th iteration of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell. 4
1, 0, 4, 99, 16, 1935, 64, 32319, 256, 522495, 1024, 8381439, 4096, 134189055, 16384, 2147368959, 65536, 34359279615, 262144, 549753978879, 1048576, 8796085682175, 4194304, 140737458995199, 16777216, 2251799696244735, 67108864, 36028796549201919, 268435456 (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

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) = 21*a(n-2) - 84*a(n-4) + 64*a(n-6) for n>5.

G.f.: (1-17*x^2+99*x^3+16*x^4-144*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).

(End)

EXAMPLE

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

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

              1                ->               1  =     1

            . . 0              ->               0  =     0

          . . 1 0 0            ->             100  =     4

        1 1 0 0 0 1 1          ->         1100011  =    99

      . . . . 1 0 0 0 0        ->           10000  =    16

    1 1 1 1 0 0 0 1 1 1 1      ->     11110001111  =  1935

  . . . . . . 1 0 0 0 0 0 0    ->         1000000  =    64

1 1 1 1 1 1 0 0 0 1 1 1 1 1 1  -> 111111000111111  = 32319

(End)

MATHEMATICA

rule = 1; 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. A265718, A265720, A059841, A056830, A000975, A265722, A128918, A265723, A265724.

Sequence in context: A024384 A320358 A180830 * A224475 A091268 A326085

Adjacent sequences:  A265718 A265719 A265720 * A265722 A265723 A265724

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 14 2015

STATUS

approved

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Last modified July 27 02:39 EDT 2021. Contains 346302 sequences. (Running on oeis4.)