A266299 Binary representation of the n-th iteration of the "Rule 14" elementary cellular automaton starting with a single ON (black) cell.

1, 110, 11000, 1100000, 110000000, 11000000000, 1100000000000, 110000000000000, 11000000000000000, 1100000000000000000, 110000000000000000000, 11000000000000000000000, 1100000000000000000000000, 110000000000000000000000000, 11000000000000000000000000000

Offset

0,2

Comments

Rules 46, 142 and 174 also generate this sequence.

Links

Robert Price, Table of n, a(n) for n = 0..999

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 (100).

Formula

From Colin Barker, Dec 28 2015 and Apr 14 2019: (Start)

a(n) = 11*10^(2*n-1) for n>0.

a(n) = 100*a(n-1) for n>1.

G.f.: (1+10*x) / (1-100*x).

(End)

a(n) = floor(110*100^(n-1)). - Karl V. Keller, Jr., Aug 30 2021

Mathematica

rule=14; 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 *) Table[FromDigits[catri[[k]]], {k, 1, rows}]   (* Binary Representation of Rows *)
LinearRecurrence[{100}, {1, 110}, 20] (* Harvey P. Dale, Aug 27 2023 *)

Prog

(Python) print([int(110*100**(n-1)) for n in range(50)]) # Karl V. Keller, Jr., Aug 30 2021

Crossrefs

Cf. A164908, A266298.

Sequence in context: A265319 A267854 A135645 * A265696 A267535 A267577

Adjacent sequences: A266296 A266297 A266298 * A266300 A266301 A266302

Keyword

nonn,easy

Author

Robert Price, Dec 26 2015

Status

approved