A099814 Bisection of A002275.

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

Offset: 0

Author

N. J. A. Sloane, Nov 19 2004

Keywords

• nonn
• easy

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

• 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).

Crossrefs

Cf. A002275, A100706 (other bisection).

Programs

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 *)

Python

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

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)

Extensions

More terms from Stefan Steinerberger, Apr 29 2006