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A266299 Binary representation of the n-th iteration of the "Rule 14" elementary cellular automaton starting with a single ON (black) cell. 3
1, 110, 11000, 1100000, 110000000, 11000000000, 1100000000000, 110000000000000, 11000000000000000, 1100000000000000000, 110000000000000000000, 11000000000000000000000, 1100000000000000000000000, 110000000000000000000000000, 11000000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Rules 46, 142 and 174 also generate 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 28 2015 and Apr 14 2019: (Start)

a(n) = 11*10^(2*n-1) for n>0.

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

G.f.: (1+10*x) / (1-100*x).

(End)

MATHEMATICA

rule=14; 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. A266298.

Sequence in context: A265319 A267854 A135645 * A265696 A267535 A267577

Adjacent sequences:  A266296 A266297 A266298 * A266300 A266301 A266302

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 26 2015

EXTENSIONS

Conjectures from Colin Barker, Apr 14 2019

STATUS

approved

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Last modified July 14 21:41 EDT 2020. Contains 335737 sequences. (Running on oeis4.)