A267035 Binary representation of the n-th iteration of the "Rule 85" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 10000, 111111, 100000000, 1111111111, 1000000000000, 11111111111111, 10000000000000000, 111111111111111111, 100000000000000000000, 1111111111111111111111, 1000000000000000000000000, 11111111111111111111111111, 10000000000000000000000000000

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 11 2016 and Apr 19 2019: (Start)

a(n) = 10001*a(n-2)-10000*a(n-4) for n>3.

G.f.: (1+11*x-x^2+1100*x^3) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

Mathematica

rule=85; 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. A267034, A267036.

Sequence in context: A286695 A286019 A286647 * A204574 A267801 A050647

Adjacent sequences: A267032 A267033 A267034 * A267036 A267037 A267038

Keyword

nonn,easy

Author

Robert Price, Jan 09 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022

Status

approved