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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

Index entries for linear recurrences with constant coefficients, signature (100).

FORMULA

From Colin Barker, Dec 28 2015: (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 *)

PROG

(PARI) Vec((1+10*x)/(1-100*x) + O(x^100)) \\ Colin Barker, Dec 28 2015

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

STATUS

approved

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Last modified March 24 11:34 EDT 2019. Contains 321448 sequences. (Running on oeis4.)