A266720 Binary representation of the middle column of the "Rule 59" elementary cellular automaton starting with a single ON (black) cell.

1, 10, 101, 1011, 10110, 101101, 1011010, 10110101, 101101010, 1011010101, 10110101010, 101101010101, 1011010101010, 10110101010101, 101101010101010, 1011010101010101, 10110101010101010, 101101010101010101, 1011010101010101010, 10110101010101010101

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

Index entries for linear recurrences with constant coefficients, signature (10,1,-10).

Formula

From Colin Barker, Jan 04 2016 and Apr 18 2019: (Start)

a(n) = (-450*(-1)^n+10009*10^n-550)/9900 for n>1.

a(n) = 10*a(n-1)+a(n-2)-10*a(n-3) for n>4.

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

(End)

a(n) = floor(10009*10^n/9900). - Karl V. Keller, Jr., Oct 17 2021

Mathematica

rule=59; 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 *)

Prog

(Python) print([10009*10**n//9900 for n in range(50)]) # Karl V. Keller, Jr., Oct 18 2021

Crossrefs

Cf. A266716, A266719, A266721.

Sequence in context: A284137 A284179 A096883 * A033128 A094945 A190480

Adjacent sequences: A266717 A266718 A266719 * A266721 A266722 A266723

Keyword

nonn,easy

Author

Robert Price, Jan 03 2016

Status

approved