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A267777 Binary representation of the n-th iteration of the "Rule 209" elementary cellular automaton starting with a single ON (black) cell. 1
1, 1, 11001, 1111001, 111111001, 11111111001, 1111111111001, 111111111111001, 11111111111111001, 1111111111111111001, 111111111111111111001, 11111111111111111111001, 1111111111111111111111001, 111111111111111111111111001, 11111111111111111111111111001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Rule 241 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..1000

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, Jan 20 2016 and Apr 20 2019: (Start)

a(n) = 101*a(n-1)-100*a(n-2) for n>2.

G.f.: (1-100*x+11000*x^2) / ((1-x)*(1-100*x)).

(End)

MATHEMATICA

rule=209; 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. A267776, A141722.

Sequence in context: A352751 A266983 A227865 * A034712 A178586 A045152

Adjacent sequences:  A267774 A267775 A267776 * A267778 A267779 A267780

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 20 2016

EXTENSIONS

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

STATUS

approved

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Last modified August 10 13:12 EDT 2022. Contains 356039 sequences. (Running on oeis4.)