A155671 a(n) = 10^n - 9^n + 1^n.

1, 2, 20, 272, 3440, 40952, 468560, 5217032, 56953280, 612579512, 6513215600, 68618940392, 717570463520, 7458134171672, 77123207545040, 794108867905352, 8146979811148160, 83322818300333432, 849905364703000880

Offset: 0

Author

Mohammad K. Azarian, Feb 01 2009

Keywords

• nonn
• easy

Comments

a(n) is the number of numbers from 1 to 10^n containing a 1 in their decimal expansion. - Charles R Greathouse IV, Mar 25 2009

Links

• Index entries for linear recurrences with constant coefficients, signature (20,-109,90).

Crossrefs

Equals A016189 + 1. See that entry for more information.

Cf. A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666, A155667, A155668, A155669, A155670.

Programs

Magma

[10^n-9^n+1: n in [0..25]]; // Wesley Ivan Hurt, Apr 21 2021

Mathematica

Table[10^n-9^n+1,{n,0,20}] (* or *) LinearRecurrence[{20,-109,90},{1,2,20},20] (* Harvey P. Dale, Nov 05 2017 *)

PARI

a(n)=10^n-9^n+1^n \\ Charles R Greathouse IV, Oct 16 2015

Formula

G.f.: 1/(1-10*x)-1/(1-9*x)+1/(1-x).

E.g.f.: e^(10*x)-e^(9*x)+e^x.

a(n) = 19*a(n-1)-90*a(n-2)+72 with a(0)=1, a(1)=2. - Vincenzo Librandi, Jul 21 2010

a(n) = 20*a(n-1)-109*a(n-2)+90*a(n-3). - Wesley Ivan Hurt, Apr 21 2021