A267524 Binary representation of the middle column of the "Rule 139" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 100, 1001, 10011, 100111, 1001111, 10011111, 100111111, 1001111111, 10011111111, 100111111111, 1001111111111, 10011111111111, 100111111111111, 1001111111111111, 10011111111111111, 100111111111111111, 1001111111111111111, 10011111111111111111

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 16 2016 and Apr 19 2019: (Start)

a(n) = 11*a(n-1) - 10*a(n-2) for n > 3. [n range correction - Karl V. Keller, Jr., Apr 08 2022]

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

(End)

Mathematica

rule=139; 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. A267520, A054135.

Sequence in context: A215254 A262863 A267156 * A259883 A242808 A304453

Adjacent sequences: A267521 A267522 A267523 * A267525 A267526 A267527

Keyword

nonn,easy

Author

Robert Price, Jan 16 2016

Status

approved