A267538 Binary representation of the middle column of the "Rule 143" elementary cellular automaton starting with a single ON (black) cell.

1, 11, 110, 1100, 11001, 110011, 1100111, 11001111, 110011111, 1100111111, 11001111111, 110011111111, 1100111111111, 11001111111111, 110011111111111, 1100111111111111, 11001111111111111, 110011111111111111, 1100111111111111111, 11001111111111111111

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 17 2016 and Apr 20 2019: (Start)

a(n) = 11*a(n-1)-10*a(n-2) for n > 4. [n range correction by Karl V. Keller, Jr., Apr 23 2022]

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

(End)

Conjecture: a(n) = floor(9901*10^n/9000). - Karl V. Keller, Jr., Apr 24 2022

Mathematica

rule=143; 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. A267533, A267539.

Sequence in context: A278664 A259661 A265699 * A278819 A274474 A272609

Adjacent sequences: A267535 A267536 A267537 * A267539 A267540 A267541

Keyword

nonn,easy

Author

Robert Price, Jan 16 2016

Status

approved