A173812 - OEIS

%I #22 Sep 09 2024 12:48:32

%S 7,87,887,8887,88887,888887,8888887,88888887,888888887,8888888887,

%T 88888888887,888888888887,8888888888887,88888888888887,

%U 888888888888887,8888888888888887,88888888888888887,888888888888888887,8888888888888888887,88888888888888888887,888888888888888888887

%N a(n) = (8*10^n - 17)/9 for n > 0.

%H Vincenzo Librandi, <a href="/A173812/b173812.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) + 17 with n > 0, a(0)=-1.

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

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

%F G.f.: x*(7+10*x)/((1-x)*(1-10*x)). (End)

%F E.g.f.: 1 + exp(x)*(8*exp(9*x) - 17)/9. - _Elmo R. Oliveira_, Sep 09 2024

%t CoefficientList[Series[(7+10*x)/((1-x)*(1-10*x)),{x,0,30}],x] (* _Vincenzo Librandi_, Jul 05 2012 *)

%t Table[FromDigits[PadLeft[{7},n,8]],{n,20}] (* _Harvey P. Dale_, Jun 22 2013 *)

%o (Magma) [(8*10^n-17)/9: n in [1..20]]; // _Vincenzo Librandi_, Jul 05 2012

%Y Cf. A093171.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 25 2010