A198399 a(n) = 9^n - 9*n.

1, 0, 63, 702, 6525, 59004, 531387, 4782906, 43046649, 387420408, 3486784311, 31381059510, 282429536373, 2541865828212, 22876792454835, 205891132094514, 1853020188851697, 16677181699666416, 150094635296998959, 1350851717672991918, 12157665459056928621, 109418989131512359020

Offset: 0

Author

Vincenzo Librandi, Oct 26 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-19,9).

Crossrefs

Cf. A005803, A107583, A107584, A107585.

Programs

Magma

[9^n-9*n: n in [0..25]];

Mathematica

CoefficientList[Series[(1 - 11*x + 82*x^2)/((1 - 9*x)*(1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)

PARI

a(n)=9^n-9*n \\ Charles R Greathouse IV, Jul 06 2017

Formula

a(0)=1, a(1)=0, a(2)=63, a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3).

G.f.: (1 - 11*x + 82*x^2)/((1 - 9*x)*(1 - x)^2). - Vincenzo Librandi, Jan 04 2013

E.g.f.: exp(x)*(exp(8*x) - 9*x). - Elmo R. Oliveira, Sep 09 2024