A267879 Binary representation of the middle column of the "Rule 233" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 101, 1010, 10101, 101011, 1010111, 10101111, 101011111, 1010111111, 10101111111, 101011111111, 1010111111111, 10101111111111, 101011111111111, 1010111111111111, 10101111111111111, 101011111111111111, 1010111111111111111, 10101111111111111111

Offset

0,2

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

Conjectures from Colin Barker, Jan 22 2016 and Apr 20 2019: (Start)

a(n) = 11*a(n-1)-10*a(n-2) for n>4.

G.f.: (1-x+x^2-x^3+x^4) / ((1-x)*(1-10*x)).

(End)

Conjecture: a(n) = (9091*10^(n-3) - 1)/9 for n > 2. - Stefano Spezia, Dec 25 2021

Mathematica

rule=233; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k]], {k, 1, rows}]  (* Binary Representation of Middle Column *)

Crossrefs

Cf. A267868.

Sequence in context: A279665 A266247 A267443 * A284137 A284179 A096883

Adjacent sequences: A267876 A267877 A267878 * A267880 A267881 A267882

Keyword

nonn,easy

Author

Robert Price, Jan 21 2016

Status

approved