A198400 a(n) = 10^n - 10*n.

1, 0, 80, 970, 9960, 99950, 999940, 9999930, 99999920, 999999910, 9999999900, 99999999890, 999999999880, 9999999999870, 99999999999860, 999999999999850, 9999999999999840, 99999999999999830, 999999999999999820, 9999999999999999810, 99999999999999999800, 999999999999999999790

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 (12,-21,10).

Crossrefs

Cf. A005803, A107583, A107584, A107585.

Programs

Magma

[10^n-10*n: n in [0..25]];

Mathematica

CoefficientList[Series[(1-12*x+101*x^2)/((1-10*x)*(1-x)^2),{x,0,40}],x] (* Vincenzo Librandi, Jul 06 2012 *)

PARI

a(n)=10^n-10*n \\ Charles R Greathouse IV, Jul 06 2017

Formula

a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 2.

G.f.: (1-12*x+101*x^2)/((1-10*x)*(1-x)^2). - Vincenzo Librandi, Jul 06 2012

E.g.f.: exp(x)*(exp(9*x) - 10*x). - Elmo R. Oliveira, Aug 29 2024