A024101 a(n) = 9^n-1.

0, 8, 80, 728, 6560, 59048, 531440, 4782968, 43046720, 387420488, 3486784400, 31381059608, 282429536480, 2541865828328, 22876792454960, 205891132094648, 1853020188851840, 16677181699666568, 150094635296999120

Offset

0,2

Comments

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

These are the numbers 888...8 in base 9. - Zerinvary Lajos, Nov 21 2007

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (10,-9).

Formula

G.f.: 1/(1-9*x)-1/(1-x). - Mohammad K. Azarian, Jan 14 2009

E.g.f.: e^(9*x)-e^x. - Mohammad K. Azarian, Jan 14 2009

a(n) = A024023(n)*A034472(n). - Reinhard Zumkeller, Feb 14 2009

a(n) = 9*a(n-1)+8 for n>0, a(0)=0. - Vincenzo Librandi, Nov 19 2010

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

a(n) = Sum_{i=1..n} 8^i*binomial(n,n-i) for n>0, a(0)=0. - Bruno Berselli, Nov 11 2015

a(n) = A001019(n) - 1. - Sean A. Irvine, Jun 19 2019

Sum_{n>=1} 1/a(n) = A248726. - Amiram Eldar, Nov 13 2020

Mathematica

Table[9^n - 1, {n, 0, 20}]
LinearRecurrence[{10, -9}, {0, 8}, 30] (* Harvey P. Dale, Apr 14 2015 *)

Prog

(PARI) a(n)=9^n-1 \\ Charles R Greathouse IV, Jun 11 2015

Crossrefs

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

Sequence in context: A182604 A320074 A290874 * A368920 A291181 A155144

Adjacent sequences: A024098 A024099 A024100 * A024102 A024103 A024104

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved