A267456 Binary representation of the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 100, 1000, 1010100, 10101000, 10101010100, 101010101000, 101010101010100, 1010101010101000, 1010101010101010100, 10101010101010101000, 10101010101010101010100, 101010101010101010101000, 101010101010101010101010100, 1010101010101010101010101000

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 15 2016 and Apr 19 2019: (Start)

a(n) = 10001*a(n-2) - 10000*a(n-4) for n > 5.

G.f.: (1+10*x)*(1 - 9901*x^2 + 20000*x^4) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)).

(End)

Mathematica

rule=133; 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. A267423, A267457.

Sequence in context: A286864 A138823 A145442 * A282580 A283013 A283057

Adjacent sequences: A267453 A267454 A267455 * A267457 A267458 A267459

Keyword

nonn,easy

Author

Robert Price, Jan 15 2016

Status

approved