A024101 - OEIS

%I #33 Nov 13 2020 03:59:53

%S 0,8,80,728,6560,59048,531440,4782968,43046720,387420488,3486784400,

%T 31381059608,282429536480,2541865828328,22876792454960,

%U 205891132094648,1853020188851840,16677181699666568,150094635296999120

%N a(n) = 9^n-1.

%C Number of integers from 0 to 10^(n+1)-1 that lack any particular digit other than 0. - _Robert G. Wilson v_, Apr 14 2003

%C These are the numbers 888...8 in base 9. - _Zerinvary Lajos_, Nov 21 2007

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).

%F G.f.: 1/(1-9*x)-1/(1-x). - _Mohammad K. Azarian_, Jan 14 2009

%F E.g.f.: e^(9*x)-e^x. - _Mohammad K. Azarian_, Jan 14 2009

%F a(n) = A024023(n)*A034472(n). - _Reinhard Zumkeller_, Feb 14 2009

%F a(n) = 9*a(n-1)+8 for n>0, a(0)=0. - _Vincenzo Librandi_, Nov 19 2010

%F a(0)=0, a(1)=8; for n>1, a(n) = 10*a(n-1)-9*a(n-2). - _Harvey P. Dale_, Apr 14 2015

%F a(n) = Sum_{i=1..n} 8^i*binomial(n,n-i) for n>0, a(0)=0. - _Bruno Berselli_, Nov 11 2015

%F a(n) = A001019(n) - 1. - _Sean A. Irvine_, Jun 19 2019

%F Sum_{n>=1} 1/a(n) = A248726. - _Amiram Eldar_, Nov 13 2020

%t Table[9^n - 1, {n, 0, 20}]

%t LinearRecurrence[{10, -9}, {0, 8}, 30] (* _Harvey P. Dale_, Apr 14 2015 *)

%o (PARI) a(n)=9^n-1 \\ _Charles R Greathouse IV_, Jun 11 2015

%Y Cf. A001019, A024023, A034472, A052386, A052379, A248726.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.