A170955 a(n) = 10^n - 9.

1, 91, 991, 9991, 99991, 999991, 9999991, 99999991, 999999991, 9999999991, 99999999991, 999999999991, 9999999999991, 99999999999991, 999999999999991, 9999999999999991, 99999999999999991, 999999999999999991, 9999999999999999991, 99999999999999999991, 999999999999999999991

Offset: 1

Author

Vincenzo Librandi, Feb 26 2010

Keywords

• nonn
• easy

Comments

Column 10 of A193871. - Omar E. Pol, Aug 22 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A093177, A193871.

Programs

Magma

[10^n-9: n in [1..30]]; // Vincenzo Librandi, Feb 06 2013

Mathematica

CoefficientList[Series[(1 + 80*x)/(1 - 11*x + 10*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *)
LinearRecurrence[{11,-10},{1,91},20] (* Harvey P. Dale, Aug 20 2015 *)
10^Range[1, 25] - 9 (* Vincenzo Librandi, Jan 03 2016 *)

PARI

a(n)=10^n-9 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 10*a(n-1) + 81 for n > 1, a(1) = 1.

G.f.: x*(1+80*x)/((10*x-1)*(x-1)). - R. J. Mathar, Aug 24 2011

From Elmo R. Oliveira, Sep 06 2024: (Start)

E.g.f.: 8 + exp(x)*(exp(9*x) - 9).

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

Extensions

Typo in formula corrected by Jon E. Schoenfield, Jun 19 2010