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A118109 Binary representation of n-th iteration of the Rule 54 elementary cellular automaton starting with a single black cell. 5
1, 111, 10001, 1110111, 100010001, 11101110111, 1000100010001, 111011101110111, 10001000100010001, 1110111011101110111, 100010001000100010001, 11101110111011101110111, 1000100010001000100010001, 111011101110111011101110111, 10001000100010001000100010001, 1110111011101110111011101110111 (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, Rule 54

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 entries for linear recurrences with constant coefficients, signature (0,10001,0,-10000).

Index to Elementary Cellular Automata

FORMULA

From Colin Barker, Dec 08 2015: (Start)

a(n) = 10001*a(n-2)-10000*a(n-4) for n>3.

G.f.: (1+111*x) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

EXAMPLE

From Michael De Vlieger, Oct 07 2015: (Start)

First 8 rows, representing ON cells as "1", OFF cells within the bounds of ON cells as "0", interpreted as a binary number at left, the decimal equivalent appearing at right:

                   1 =     1

                 111 =     7

              1 0001 =    17

            111 0111 =   119

         1 0001 0001 =   273

       111 0111 0111 =  1911

    1 0001 0001 0001 =  4369

  111 0111 0111 0111 = 30583

10001 0001 0001 0001 = 69905

(End)

MATHEMATICA

rule=54; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) Table[FromDigits[catri[[k]]], {k, 1, rows}]   (* Binary Representation of Rows *)(* Robert Price, Feb 21 2016 *)

PROG

(PARI) Vec((1+111*x)/((1-x)*(1+x)*(1-100*x)*(1+100*x)) + O(x^20)) \\ Colin Barker, Dec 14 2015

CROSSREFS

Cf. A071030 (essentially the same but lists bits separately), A118108 (converted to base 10).

Sequence in context: A286771 A284208 A266381 * A265280 A267275 A135577

Adjacent sequences:  A118106 A118107 A118108 * A118110 A118111 A118112

KEYWORD

nonn,tabf,easy

AUTHOR

Eric W. Weisstein, Apr 13 2006

EXTENSIONS

Terms changed to match definition, as suggested by Michael De Vlieger. - N. J. A. Sloane, Oct 17 2015

STATUS

approved

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Last modified November 23 21:46 EST 2017. Contains 295141 sequences.