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A267804 Binary representation of the n-th iteration of the "Rule 214" elementary cellular automaton starting with a single ON (black) cell. 1
1, 111, 10111, 1100111, 101110111, 11001100111, 1011101110111, 110011001100111, 10111011101110111, 1100110011001100111, 101110111011101110111, 11001100110011001100111, 1011101110111011101110111, 110011001100110011001100111, 10111011101110111011101110111 (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 22 2016 and Apr 20 2019: (Start)

a(n) = 10001*a(n-2)-10000*a(n-4) for n>3.

G.f.: (1+111*x+110*x^2-10000*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

MATHEMATICA

rule=214; 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. A071040.

Sequence in context: A118110 A267608 A244663 * A267925 A286504 A286404

Adjacent sequences:  A267801 A267802 A267803 * A267805 A267806 A267807

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 20 2016

STATUS

approved

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Last modified July 30 19:33 EDT 2021. Contains 346359 sequences. (Running on oeis4.)