A267457 Decimal representation of the n-th iteration of the "Rule 133" elementary cellular automaton starting with a single ON (black) cell.

1, 2, 4, 8, 84, 168, 1364, 2728, 21844, 43688, 349524, 699048, 5592404, 11184808, 89478484, 178956968, 1431655764, 2863311528, 22906492244, 45812984488, 366503875924, 733007751848, 5864062014804, 11728124029608, 93824992236884, 187649984473768

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) = 17*a(n-2)-16*a(n-4) for n>5.

G.f.: (1+2*x)*(1-13*x^2+32*x^4) / ((1-x)*(1+x)*(1-4*x)*(1+4*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]], 2], {k, 1, rows}]   (* Decimal Representation of Rows *)

Crossrefs

Cf. A267423, A267456.

Sequence in context: A018560 A087375 A018580 * A322614 A089337 A088114

Adjacent sequences: A267454 A267455 A267456 * A267458 A267459 A267460

Keyword

nonn,easy

Author

Robert Price, Jan 15 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