A099814 Bisection of A002275.

0, 11, 1111, 111111, 11111111, 1111111111, 111111111111, 11111111111111, 1111111111111111, 111111111111111111, 11111111111111111111, 1111111111111111111111, 111111111111111111111111, 11111111111111111111111111, 1111111111111111111111111111, 111111111111111111111111111111, 11111111111111111111111111111111

Offset

0,2

Comments

Except for the first term (replace 0 with 1) this is the binary representation of the n-th iteration of the elementary cellular automaton starting with a single ON (black) cell for Rule 189. - Robert Price, Feb 21 2016

Links

Table of n, a(n) for n=0..16.

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Index to Elementary Cellular Automata

Index entries for sequences related to cellular automata

Index entries for linear recurrences with constant coefficients, signature (101,-100).

Formula

For n>0, 1 repeated 2n times.

a(n) = a(n-1) + 11*100^(n-1) with a(0)=0. - Vincenzo Librandi, Nov 16 2010

a(n) = (100^n - 1)/9. - Bernard Schott, Apr 09 2023

From Stefano Spezia, Jul 27 2024: (Start)

G.f.: 11*x/((1 - x)*(1 - 100*x)).

E.g.f.: exp(x)*(exp(99*x) - 1)/9. (End)

Mathematica

Table[(10^(2n) - 1)/9, {n, 0, 20}] (* Stefan Steinerberger, Apr 29 2006 *)
Table[FromDigits[PadRight[{}, 2n, 1]], {n, 0, 20}] (* Harvey P. Dale, Jul 20 2015 *)

Prog

(Python)
def A099814(n): return (10**(n<<1)-1)//9 # Chai Wah Wu, Nov 04 2022

Crossrefs

Cf. A002275, A100706 (other bisection).

Sequence in context: A289968 A248753 A248754 * A340549 A260077 A068053

Adjacent sequences: A099811 A099812 A099813 * A099815 A099816 A099817

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 19 2004

Extensions

More terms from Stefan Steinerberger, Apr 29 2006

Status

approved