A266612 Binary representation of the middle column of the "Rule 41" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 101, 1010, 10100, 101001, 1010010, 10100101, 101001010, 1010010101, 10100101010, 101001010101, 1010010101010, 10100101010101, 101001010101010, 1010010101010101, 10100101010101010, 101001010101010101, 1010010101010101010, 10100101010101010101

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 02 2016 and Apr 17 2019: (Start)

a(n) = (-9*(-1)^n+99991*2^(n-2)*5^(n-3)-11)/198 for n>2.

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

G.f.: (1-x^4+x^5) / ((1-x)*(1+x)*(1-10*x)).

(End)

Mathematica

rule=41; 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. A266608, A266611, A266613.

Sequence in context: A281102 A123522 A303596 * A267588 A267514 A279809

Adjacent sequences: A266609 A266610 A266611 * A266613 A266614 A266615

Keyword

nonn,easy

Author

Robert Price, Jan 01 2016

Extensions

Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - N. J. A. Sloane, Jun 13 2022

Status

approved