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A267456 Binary representation of the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell. 1
1, 10, 100, 1000, 1010100, 10101000, 10101010100, 101010101000, 101010101010100, 1010101010101000, 1010101010101010100, 10101010101010101000, 10101010101010101010100, 101010101010101010101000, 101010101010101010101010100, 1010101010101010101010101000 (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..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 15 2016 and Apr 19 2019: (Start)

a(n) = 10001*a(n-2)-10000*a(n-4) for n>5.

G.f.: (1+10*x)*(1-9901*x^2+20000*x^4) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

MATHEMATICA

rule=133; 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. A267423.

Sequence in context: A286864 A138823 A145442 * A282580 A283013 A283057

Adjacent sequences:  A267453 A267454 A267455 * A267457 A267458 A267459

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 15 2016

STATUS

approved

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Last modified January 24 01:05 EST 2020. Contains 331178 sequences. (Running on oeis4.)