Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Sep 08 2022 08:45:40
%S 1,2,20,272,3440,40952,468560,5217032,56953280,612579512,6513215600,
%T 68618940392,717570463520,7458134171672,77123207545040,
%U 794108867905352,8146979811148160,83322818300333432,849905364703000880
%N a(n) = 10^n - 9^n + 1^n.
%C 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
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (20,-109,90).
%F G.f.: 1/(1-10*x)-1/(1-9*x)+1/(1-x).
%F E.g.f.: e^(10*x)-e^(9*x)+e^x.
%F a(n) = 19*a(n-1)-90*a(n-2)+72 with a(0)=1, a(1)=2. - _Vincenzo Librandi_, Jul 21 2010
%F a(n) = 20*a(n-1)-109*a(n-2)+90*a(n-3). - _Wesley Ivan Hurt_, Apr 21 2021
%t Table[10^n-9^n+1,{n,0,20}] (* or *) LinearRecurrence[{20,-109,90},{1,2,20},20] (* _Harvey P. Dale_, Nov 05 2017 *)
%o (PARI) a(n)=10^n-9^n+1^n \\ _Charles R Greathouse IV_, Oct 16 2015
%o (Magma) [10^n-9^n+1: n in [0..25]]; // _Wesley Ivan Hurt_, Apr 21 2021
%Y Equals A016189 + 1. See that entry for more information.
%Y Cf. A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666, A155667, A155668, A155669, A155670.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_, Feb 01 2009