OFFSET
1,1
COMMENTS
For n >=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,...,10} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,...,10} we have f(x)<>y. - Aleksandar M. Janjic and Milan Janjic, Mar 27 2007
For n >= 1, a(n) is the number of n-digit positive integers. - Geoffrey Critzer, Apr 23 2009
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Miklos Bona, Introduction to Enumerative Combinatorics, McGraw-Hill, 2007, p. 8.
LINKS
FORMULA
a(n) = 9*10^(n-1), n >= 1.
From Stefano Spezia, Jun 03 2021: (Start)
O.g.f.: 9*x/(1 - 10*x).
E.g.f.: 9*(exp(10*x) - 1)/10.
a(n) = 10*a(n-1) for n > 1. (End)
MATHEMATICA
q = 10; Join[{a = 1}, Table[If[n == 0, a = q * a - 1, a = q * a], {n, 0, 25}]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
Differences[10^Range[0, 19]] (* Alonso del Arte, Feb 23 2015 *)
PROG
(PARI) a(n)=9*10^(n-1) \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Feb 03 2000
EXTENSIONS
Deleted erroneous term a(0)=1. - N. J. A. Sloane, Apr 02 2015
STATUS
approved