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A266838 Binary representation of the n-th iteration of the "Rule 67" elementary cellular automaton starting with a single ON (black) cell. 1
1, 100, 1010, 1100001, 1011100, 11100001011, 1011100000, 111100001011111, 1011100000000, 1111100001011111111, 1011100000000000, 11111100001011111111111, 1011100000000000000, 111111100001011111111111111, 1011100000000000000000, 1111111100001011111111111111111 (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 05 2016 and Apr 18 2019: (Start)

a(n) = 11001*a(n-2)-10011000*a(n-4)+10000000*a(n-6) for n>9.

G.f.: (1 +100*x -9991*x^2 -99*x^3 -88910*x^4 -9990*x^5 -10901100*x^6 -99900*x^7 +11000000*x^8 -1000000*x^9) / ((1 -x)*(1 +x)*(1 -100*x)*(1 +100*x)*(1 -1000*x^2)).

(End)

MATHEMATICA

rule=67; 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. A266837.

Sequence in context: A173484 A136387 A001737 * A267127 A266893 A267153

Adjacent sequences:  A266835 A266836 A266837 * A266839 A266840 A266841

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 04 2016

STATUS

approved

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Last modified September 22 00:42 EDT 2020. Contains 337276 sequences. (Running on oeis4.)