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

1,2

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).

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)

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 *)

Prog

(Magma) [10^n-9: n in [1..30]]; // Vincenzo Librandi, Feb 06 2013
(PARI) a(n)=10^n-9 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A093177, A193871.

Sequence in context: A254519 A185375 A036526 * A020316 A221815 A195221

Adjacent sequences: A170952 A170953 A170954 * A170956 A170957 A170958

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 26 2010

Extensions

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

Status

approved