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A052386
Number of integers from 1 to 10^n-1 that lack 0 as a digit.
12
0, 9, 90, 819, 7380, 66429, 597870, 5380839, 48427560, 435848049, 3922632450, 35303692059, 317733228540, 2859599056869, 25736391511830, 231627523606479, 2084647712458320, 18761829412124889, 168856464709124010, 1519708182382116099, 13677373641439044900
OFFSET
0,2
FORMULA
a(n) = 9*a(n-1) + 9.
a(n) = 9*(9^n-1)/8 = sum_{j=1..n} 9^j = a(n-1)+9^n = 9*A002452(n) = A002452(n+1)-1; write A000918(n+1) in base 2 and read as if written in base 9. - Henry Bottomley, Aug 30 2001
a(n) = 10*a(n-1)-9*a(n-2). G.f.: 9*x / ((x-1)*(9*x-1)). - Colin Barker, Sep 26 2013
EXAMPLE
For n=2, the numbers from 1 to 99 which *have* 0 as a digit are the 9 numbers 10, 20, 30, ..., 90. So a(1) = 99 - 9 = 90.
MATHEMATICA
Table[9(9^n - 1)/8, {n, 0, 20}]
LinearRecurrence[{10, -9}, {0, 9}, 30] (* Harvey P. Dale, Mar 22 2019 *)
PROG
(Magma) [9*(9^n-1)/8: n in [0..20]]; // Vincenzo Librandi, Jul 04 2011
(PARI) a(n)=9^(n+1)\8 \\ Charles R Greathouse IV, Aug 25 2014
CROSSREFS
Row n=9 of A228275.
Sequence in context: A270242 A054616 A344068 * A246941 A186510 A158609
KEYWORD
easy,nonn,base
AUTHOR
Odimar Fabeny, Mar 10 2000
EXTENSIONS
More terms and revised description from James A. Sellers, Mar 13 2000
More terms and revised description from Robert G. Wilson v, Apr 14 2003
More terms from Colin Barker, Sep 26 2013
STATUS
approved