A266717 Binary representation of the n-th iteration of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.

1, 101, 110, 1111011, 1100, 11111110111, 11000, 111111111101111, 110000, 1111111111111011111, 1100000, 11111111111111110111111, 11000000, 111111111111111111101111111, 110000000, 1111111111111111111111011111111, 1100000000, 11111111111111111111111110111111111

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 04 2016 and Apr 18 2019: (Start)

a(n) = 10011*a(n-2)-110010*a(n-4)+100000*a(n-6) for n>6.

G.f.: (1+101*x-9901*x^2+99900*x^3-990100*x^4-110000*x^5+1000000*x^6) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-10*x^2)).

(End)

Mathematica

rule=59; 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. A266716, A266718.

Sequence in context: A290725 A255966 A305396 * A303571 A303573 A050661

Adjacent sequences: A266714 A266715 A266716 * A266718 A266719 A266720

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Extensions

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

Status

approved