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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..500 Index entries for linear recurrences with constant coefficients, signature (10,-9). 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 Cf. A024101, A052379. Row n=9 of A228275. Sequence in context: A261315 A270242 A054616 * A246941 A186510 A158609 Adjacent sequences:  A052383 A052384 A052385 * A052387 A052388 A052389 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

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Last modified July 20 12:29 EDT 2019. Contains 325180 sequences. (Running on oeis4.)