A165247 a(n) = (10^n + 71)/9.
9, 19, 119, 1119, 11119, 111119, 1111119, 11111119, 111111119, 1111111119, 11111111119, 111111111119, 1111111111119, 11111111111119, 111111111111119, 1111111111111119, 11111111111111119, 111111111111111119, 1111111111111111119, 11111111111111111119, 111111111111111111119
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..100
- Markus Tervooren, Factorizations of (1)w9.
- Index entries for linear recurrences with constant coefficients, signature (11,-10).
Programs
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Mathematica
Table[FromDigits[PadLeft[{9}, n, 1]], {n, 20}] (* Harvey P. Dale, Apr 25 2014 *) CoefficientList[Series[(9 - 80 x)/((1 - x) (1 - 10 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 26 2014 *) (10^Range[20] + 71)/9 (* Alonso del Arte, Apr 18 2015 *)
Formula
G.f.: x*(9 - 80*x)/((1 - x)*(1 - 10*x)). - Vincenzo Librandi, Apr 26 2014
From Elmo R. Oliveira, Jun 17 2025: (Start)
E.g.f.: -8 + exp(x)*(71 + exp(9*x))/9.
a(n) = 11*a(n-1) - 10*a(n-2) for n >= 3. (End)
Comments