login
a(n) = (8*10^n - 53)/9 for n > 0.
2

%I #25 Sep 09 2024 20:38:36

%S 3,83,883,8883,88883,888883,8888883,88888883,888888883,8888888883,

%T 88888888883,888888888883,8888888888883,88888888888883,

%U 888888888888883,8888888888888883,88888888888888883,888888888888888883,8888888888888888883,88888888888888888883,888888888888888888883

%N a(n) = (8*10^n - 53)/9 for n > 0.

%H Vincenzo Librandi, <a href="/A173811/b173811.txt">Table of n, a(n) for n = 1..100</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F a(n) = 10*a(n-1) + 53 for n > 0, a(0) = -5.

%F From _Vincenzo Librandi_, Jul 05 2012: (Start)

%F G.f.: x*(3+50*x)/((1-x)*(1-10*x)).

%F a(n) = 11*a(n-1) - 10*a(n-2). (End)

%F E.g.f.: exp(x)*(8*exp(9*x) - 53)/9. - _Elmo R. Oliveira_, Sep 09 2024

%t NestList[10#+53&,3,20] (* _Harvey P. Dale_, Jun 13 2011 *)

%t CoefficientList[Series[(3+50*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* _Vincenzo Librandi_, Jul 05 2012 *)

%o (Magma)[(8*10^n-53)/9: n in [1..20]]; // _Vincenzo Librandi_, Jul 05 2012

%Y Cf. A093166.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 25 2010