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

0,2

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).

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: A270242 A054616 A344068 * 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