A267359 Binary representation of the n-th iteration of the "Rule 125" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 11100, 101111, 111110000, 1000111111, 1111101000000, 10001111111111, 11111010000000000, 100011111111111111, 111110100000000000000, 1000111111111111111111, 1111101000000000000000000, 10001111111111111111111111, 11111010000000000000000000000

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 14 2016 and Apr 19 2019: (Start)

a(n) = 10001*a(n-2) - 10000*a(n-4) for n > 8.

G.f.: (1 + 11*x + 1099*x^2 - 8900*x^3 + 108900*x^4 - 10990000*x^5 + 890000*x^6 + 11000000*x^7 - 1000000*x^8) / ((1 - x)*(1 + x)*(1 - 100*x)*(1 + 100*x)).

(End)

Mathematica

rule=125; 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. A267358, A267360.

Sequence in context: A068223 A068224 A066945 * A267940 A113615 A034873

Adjacent sequences: A267356 A267357 A267358 * A267360 A267361 A267362

Keyword

nonn,easy

Author

Robert Price, Jan 13 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