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a(n) = (10^n + 71)/9.
3

%I #19 Jun 30 2023 14:20:55

%S 9,19,119,1119,11119,111119,1111119,11111119,111111119,1111111119,

%T 11111111119,111111111119,1111111111119,11111111111119,

%U 111111111111119,1111111111111119,11111111111111119

%N a(n) = (10^n + 71)/9.

%C Also n - 1 ones followed by a nine.

%H Vincenzo Librandi, <a href="/A165247/b165247.txt">Table of n, a(n) for n = 1..100</a>

%H Markus Tervooren, <a href="http://factordb.com/search.php?query=%2810%5Ex%2B71%29%2F9">Factorizations of (1)w9</a>

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

%F G.f.: x*(9 - 80*x)/((1 - x)*(1 - 10*x)). - _Vincenzo Librandi_, Apr 26 2014

%t Table[FromDigits[PadLeft[{9}, n, 1]], {n, 20}] (* _Harvey P. Dale_, Apr 25 2014 *)

%t CoefficientList[Series[(9 - 80 x)/((1 - x) (1 - 10 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Apr 26 2014 *)

%t (10^Range[20] + 71)/9 (* _Alonso del Arte_, Apr 18 2015 *)

%Y Cf. A104482, A093400.

%K easy,nonn

%O 1,1

%A _Ivan Panchenko_, Sep 10 2009