A133383 - OEIS

%I #25 Jun 14 2025 00:27:01

%S 10,1099,109999,10999999,1099999999,109999999999,10999999999999,

%T 1099999999999999,109999999999999999,10999999999999999999,

%U 1099999999999999999999,109999999999999999999999,10999999999999999999999999,1099999999999999999999999999,109999999999999999999999999999

%N 10 followed by 2n 9's.

%H Vincenzo Librandi, <a href="/A133383/b133383.txt">Table of n, a(n) for n = 0..200</a>

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

%F a(n) = 11*10^(2*n) - 1. -  _Vincenzo Librandi_, Aug 10 2011

%F From _Elmo R. Oliveira_, Jun 12 2025: (Start)

%F G.f.: (10 + 89*x)/((100*x-1)*(x-1)).

%F E.g.f.: exp(x)*(11*exp(99*x) - 1).

%F a(n) = 101*a(n-1) - 100*a(n-2). (End)

%t 11*10^(2*Range[15]) - 1 (* _Paolo Xausa_, Jun 13 2025 *)

%o (Magma) [11*10^(2*n)-1: n in [0..15]]; // _Vincenzo Librandi_, Aug 10 2011

%K nonn,base,easy

%O 0,1

%A _Paul Curtz_, Oct 29 2007