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

Author

Ivan Panchenko, Sep 10 2009

Keywords

• easy
• nonn

Comments

Also n - 1 ones followed by a nine.

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).

Crossrefs

Cf. A093400, A104482.

Programs

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)