cp's OEIS Frontend

A099814 Bisection of A002275.

%I A099814 #31 Feb 16 2025 08:32:55
%S A099814 0,11,1111,111111,11111111,1111111111,111111111111,11111111111111,
%T A099814 1111111111111111,111111111111111111,11111111111111111111,
%U A099814 1111111111111111111111,111111111111111111111111,11111111111111111111111111,1111111111111111111111111111,111111111111111111111111111111,11111111111111111111111111111111
%N A099814 Bisection of A002275.
%C A099814 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 A099814 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A099814 Stephen Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>, Wolfram Media, 2002; p. 55.
%H A099814 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A099814 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A099814 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).
%F A099814 For n>0, 1 repeated 2n times.
%F A099814 a(n) = a(n-1) + 11*100^(n-1) with a(0)=0. - _Vincenzo Librandi_, Nov 16 2010
%F A099814 a(n) = (100^n - 1)/9. - _Bernard Schott_, Apr 09 2023
%F A099814 From _Stefano Spezia_, Jul 27 2024: (Start)
%F A099814 G.f.: 11*x/((1 - x)*(1 - 100*x)).
%F A099814 E.g.f.: exp(x)*(exp(99*x) - 1)/9. (End)
%t A099814 Table[(10^(2n) - 1)/9, {n, 0, 20}] (* _Stefan Steinerberger_, Apr 29 2006 *)
%t A099814 Table[FromDigits[PadRight[{},2n,1]],{n,0,20}] (* _Harvey P. Dale_, Jul 20 2015 *)
%o A099814 (Python)
%o A099814 def A099814(n): return (10**(n<<1)-1)//9 # _Chai Wah Wu_, Nov 04 2022
%Y A099814 Cf. A002275, A100706 (other bisection).
%K A099814 nonn,easy
%O A099814 0,2
%A A099814 _N. J. A. Sloane_, Nov 19 2004
%E A099814 More terms from _Stefan Steinerberger_, Apr 29 2006