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A266254 Binary representation of the n-th iteration of the "Rule 11" elementary cellular automaton starting with a single ON (black) cell. 3
1, 100, 11, 1111100, 11, 11111111100, 11, 111111111111100, 11, 1111111111111111100, 11, 11111111111111111111100, 11, 111111111111111111111111100, 11, 1111111111111111111111111111100, 11, 11111111111111111111111111111111100, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Rule 43 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 26 2015 and Apr 14 2019: (Start)

a(n) = (199*(-1)^n+10^(2*n+1)-(-1)^n*10^(2*n+1)-1)/18 for n>0.

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

G.f.: (1+100*x-9990*x^2+111000*x^3-100000*x^4) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

MATHEMATICA

rule=11; 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 *)

CROSSREFS

Cf. A266253.

Sequence in context: A287715 A286639 A288358 * A298574 A077489 A153674

Adjacent sequences:  A266251 A266252 A266253 * A266255 A266256 A266257

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 25 2015

EXTENSIONS

Conjectures from Colin Barker, Apr 14 2019

STATUS

approved

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Last modified May 27 13:00 EDT 2020. Contains 334657 sequences. (Running on oeis4.)