A266838 Binary representation of the n-th iteration of the "Rule 67" elementary cellular automaton starting with a single ON (black) cell.

1, 100, 1010, 1100001, 1011100, 11100001011, 1011100000, 111100001011111, 1011100000000, 1111100001011111111, 1011100000000000, 11111100001011111111111, 1011100000000000000, 111111100001011111111111111, 1011100000000000000000, 1111111100001011111111111111111

Offset

0,2

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

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)

Conjecture: a(n) = (10*100^n - 999909*1000^floor(n/2)/10000 - 1)/9 for odd n > 3; a(n) = 10111*1000^(n/2)/10000 for even n > 3. - Karl V. Keller, Jr., Dec 16 2021

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, A266839.

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