A267588 Binary representation of the middle column of the "Rule 169" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 101, 1010, 10100, 101001, 1010011, 10100111, 101001111, 1010011111, 10100111111, 101001111111, 1010011111111, 10100111111111, 101001111111111, 1010011111111111, 10100111111111111, 101001111111111111, 1010011111111111111, 10100111111111111111

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 18 2016 and Apr 20 2019: (Start)

a(n) = 11*a(n-1)-10*a(n-2) for n>3.

G.f.: (1-x+x^2-x^3+x^5) / ((1-x)*(1-10*x)).

(End)

Mathematica

rule=169; 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. A264442.

Sequence in context: A123522 A303596 A266612 * A267514 A279809 A279749

Adjacent sequences: A267585 A267586 A267587 * A267589 A267590 A267591

Keyword

nonn,easy

Author

Robert Price, Jan 18 2016

Status

approved