A198700 a(n) = 11*10^n - 1.
10, 109, 1099, 10999, 109999, 1099999, 10999999, 109999999, 1099999999, 10999999999, 109999999999, 1099999999999, 10999999999999, 109999999999999, 1099999999999999, 10999999999999999, 109999999999999999, 1099999999999999999, 10999999999999999999, 109999999999999999999
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (11,-10).
Programs
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Magma
[11*10^n-1: n in [0..30]];
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Mathematica
(11 10^Range[0,20])-1 (* or *) LinearRecurrence[{11,-10},{10,109},20] (* Harvey P. Dale, Nov 29 2020 *)
Formula
a(n) = 10*a(n-1) + 9.
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: (10-x)/((10*x-1)*(x-1)). - R. J. Mathar, Oct 29 2011
E.g.f.: exp(x)*(11*exp(9*x) - 1). - Elmo R. Oliveira, Aug 23 2024