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%I #18 Mar 04 2024 01:14:34
%S 10,99,989,9889,98889,988889,9888889,98888889,988888889,9888888889,
%T 98888888889,988888888889,9888888888889,98888888888889,
%U 988888888888889,9888888888888889,98888888888888889,988888888888888889,9888888888888888889,98888888888888888889
%N a(1)=10; a(n) = a(n-1)*10 - 1.
%C For n -> oo, a(n)/10^n -> 0.9888......8889 = 89/90.
%H Colin Barker, <a href="/A179555/b179555.txt">Table of n, a(n) for n = 1..999</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F From _Colin Barker_, Oct 03 2015: (Start)
%F a(n) = 11*a(n-1) - 10*a(n-2) for n>2.
%F G.f.: -x*(11*x-10) / ((x-1)*(10*x-1)).
%F (End)
%t a[1] := 10; a[n_] := a[n] = 10 a[n - 1] - 1; Array[a@ # &, {20}] (* _Michael De Vlieger_, Oct 03 2015 *)
%o (PARI) Vec(-x*(11*x-10)/((x-1)*(10*x-1)) + O(x^30)) \\ _Colin Barker_, Oct 03 2015
%K nonn,easy
%O 1,1
%A _Mark Dols_, Jul 19 2010
%E Name edited by _Colin Barker_, Oct 03 2015