A052386 Number of integers from 1 to 10^n-1 that lack 0 as a digit.
0, 9, 90, 819, 7380, 66429, 597870, 5380839, 48427560, 435848049, 3922632450, 35303692059, 317733228540, 2859599056869, 25736391511830, 231627523606479, 2084647712458320, 18761829412124889, 168856464709124010, 1519708182382116099, 13677373641439044900
Offset: 0
Examples
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.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..500
- Peter D. Loly and Ian D. Cameron, Frierson's 1907 Parameterization of Compound Magic Squares Extended to Orders 3^L, L = 1, 2, 3, ..., with Information Entropy, arXiv:2008.11020 [math.HO], 2020.
- Index entries for linear recurrences with constant coefficients, signature (10,-9).
Programs
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Magma
[9*(9^n-1)/8: n in [0..20]]; // Vincenzo Librandi, Jul 04 2011
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Mathematica
Table[9(9^n - 1)/8, {n, 0, 20}] LinearRecurrence[{10,-9},{0,9},30] (* Harvey P. Dale, Mar 22 2019 *) -
PARI
a(n)=9^(n+1)\8 \\ Charles R Greathouse IV, Aug 25 2014
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
Extensions
More terms and revised description from James 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