A267779 Binary representation of the n-th iteration of the "Rule 211" elementary cellular automaton starting with a single ON (black) cell.

1, 101, 11001, 1111101, 111111001, 11111111101, 1111111111001, 111111111111101, 11111111111111001, 1111111111111111101, 111111111111111111001, 11111111111111111111101, 1111111111111111111111001, 111111111111111111111111101, 11111111111111111111111111001

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 20 2016 and Apr 20 2019: (Start)

a(n) = 100*a(n-1) + a(n-2) - 100*a(n-3) for n > 3.

G.f.: (1 + x + 900*x^2 + 11000*x^3) / ((1-x)*(1+x)*(1-100*x)).

(End)

Mathematica

rule=211; 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. A267778, A267780.

Sequence in context: A100027 A097727 A083981 * A138148 A138831 A267920

Adjacent sequences: A267776 A267777 A267778 * A267780 A267781 A267782

Keyword

nonn,easy

Author

Robert Price, Jan 20 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. - N. J. A. Sloane, Jun 13 2022

Status

approved