A267523 Binary representation of the n-th iteration of the "Rule 139" elementary cellular automaton starting with a single ON (black) cell.

1, 100, 10011, 1001111, 100111111, 10011111111, 1001111111111, 100111111111111, 10011111111111111, 1001111111111111111, 100111111111111111111, 10011111111111111111111, 1001111111111111111111111, 100111111111111111111111111, 10011111111111111111111111111, 1001111111111111111111111111111

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 (101,-100).

Formula

From Colin Barker, Jan 16 2016: (Start)

a(n) = 101*a(n-1)-100*a(n-2) for n>2.

G.f.: (1-x+11*x^2) / ((1-x)*(1-100*x)). (End)

a(n) = 100^n + floor(100^(n-1)/9). - Karl V. Keller, Jr., Sep 15 2021

E.g.f.: (99 - 100*exp(x) + 901*exp(100*x))/900. - Stefano Spezia, Aug 05 2024

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 *) Table[FromDigits[catri[[k]]], {k, 1, rows}] (* Binary Representation of Rows *)

Prog

(Python) print([100**n + int(100**(n-1))//9  for n in range(50)]) # Karl V. Keller, Jr., Sep 15 2021

Crossrefs

Cf. A267520.

Sequence in context: A096885 A267449 A266752 * A027576 A099374 A233627

Adjacent sequences: A267520 A267521 A267522 * A267524 A267525 A267526

Keyword

nonn,easy

Author

Robert Price, Jan 16 2016

Status

approved