A024115 a(n) = 10^n - n.

1, 9, 98, 997, 9996, 99995, 999994, 9999993, 99999992, 999999991, 9999999990, 99999999989, 999999999988, 9999999999987, 99999999999986, 999999999999985, 9999999999999984, 99999999999999983, 999999999999999982, 9999999999999999981, 99999999999999999980, 999999999999999999979

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (12,-21,10).

Crossrefs

Cf. numbers of the form k^n-n: A000325 (k=2), A024024 (k=3), A024037 (k=4), A024050 (k=5), A024063 (k=6), A024076 (k=7), A024089 (k=8), A024102 (k=9), this sequence (k=10), A024128 (k=11), A024141 (k=12).

Programs

Magma

[10^n-n: n in [0..20]]; // Vincenzo Librandi, Jun 30 2011

Magma

I:=[1, 9, 98]; [n le 3 select I[n] else 12*Self(n-1)-21*Self(n-2)+10*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2013

Mathematica

Table[10^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 11 x^2) / ((1 - 10 x) (1 - x)^2),{x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2013 *)
LinearRecurrence[{12,-21,10},{1,9,98},20] (* Harvey P. Dale, Jul 18 2020 *)

PARI

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

Formula

From Vincenzo Librandi, Jun 17 2013: (Start)

G.f.: (1-3*x+11*x^2)/((1-10*x)*(1-x)^2).

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

E.g.f.: exp(x)*(exp(9*x) - x). - Elmo R. Oliveira, Sep 06 2024