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Bisection of A002275.
8

%I #30 Jul 27 2024 14:10:02

%S 0,11,1111,111111,11111111,1111111111,111111111111,11111111111111,

%T 1111111111111111,111111111111111111,11111111111111111111,

%U 1111111111111111111111,111111111111111111111111,11111111111111111111111111,1111111111111111111111111111,111111111111111111111111111111,11111111111111111111111111111111

%N Bisection of A002275.

%C 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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).

%F For n>0, 1 repeated 2n times.

%F a(n) = a(n-1) + 11*100^(n-1) with a(0)=0. - _Vincenzo Librandi_, Nov 16 2010

%F a(n) = (100^n - 1)/9. - _Bernard Schott_, Apr 09 2023

%F From _Stefano Spezia_, Jul 27 2024: (Start)

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

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

%t Table[(10^(2n) - 1)/9, {n, 0, 20}] (* _Stefan Steinerberger_, Apr 29 2006 *)

%t Table[FromDigits[PadRight[{},2n,1]],{n,0,20}] (* _Harvey P. Dale_, Jul 20 2015 *)

%o (Python)

%o def A099814(n): return (10**(n<<1)-1)//9 # _Chai Wah Wu_, Nov 04 2022

%Y Cf. A002275, A100706 (other bisection).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 19 2004

%E More terms from _Stefan Steinerberger_, Apr 29 2006