A267350 Binary representation of the n-th iteration of the "Rule 123" elementary cellular automaton starting with a single ON (black) cell.

1, 101, 1110, 1110111, 111000, 11111011111, 11100000, 111111101111111, 1110000000, 1111111110111111111, 111000000000, 11111111111011111111111, 11100000000000, 111111111111101111111111111, 1110000000000000, 1111111111111110111111111111111, 111000000000000000

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: (Start)

a(n) = 10101*a(n-2) - 1010100*a(n-4) + 1000000*a(n-6) for n > 6.

G.f.: (1 + 101*x - 8991*x^2 + 89910*x^3 - 10091010*x^4 - 200000*x^5 + 10100000*x^6) / ((1-x)*(1+x)*(1-10*x)*(1+10*x)*(1-100*x)*(1+100*x)).

(End)

Mathematica

rule=123; 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. A267349, A267351.

Sequence in context: A280340 A283589 A284403 * A290526 A290827 A290835

Adjacent sequences: A267347 A267348 A267349 * A267351 A267352 A267353

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