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A266179 Binary representation of the n-th iteration of the "Rule 6" elementary cellular automaton starting with a single ON (black) cell. 6
1, 110, 10000, 1100000, 100000000, 11000000000, 1000000000000, 110000000000000, 10000000000000000, 1100000000000000000, 100000000000000000000, 11000000000000000000000, 1000000000000000000000000, 110000000000000000000000000, 10000000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Rules 38,134 and 166 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 23 2015 and Apr 13 2019: (Start)

a(n) = 4^(n-1)*5^(2*n-1)*(21-(-1)^n).

a(n) = 10000*a(n-2) for n>1.

G.f.: (1+110*x) / ((1-100*x)*(1+100*x)).

(End)

MATHEMATICA

rule=6; 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. A266179.

Sequence in context: A111784 A146495 A063751 * A163664 A266844 A265319

Adjacent sequences:  A266176 A266177 A266178 * A266180 A266181 A266182

KEYWORD

nonn,easy,changed

AUTHOR

Robert Price, Dec 22 2015

EXTENSIONS

Conjectures from Colin Barker, Apr 13 2019

STATUS

approved

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Last modified April 24 00:02 EDT 2019. Contains 322404 sequences. (Running on oeis4.)