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A052386 Number of integers from 1 to 10^n-1 that lack 0 as a digit.

%I A052386 #34 Jul 02 2025 16:01:58
%S A052386 0,9,90,819,7380,66429,597870,5380839,48427560,435848049,3922632450,
%T A052386 35303692059,317733228540,2859599056869,25736391511830,
%U A052386 231627523606479,2084647712458320,18761829412124889,168856464709124010,1519708182382116099,13677373641439044900
%N A052386 Number of integers from 1 to 10^n-1 that lack 0 as a digit.
%H A052386 Vincenzo Librandi, <a href="/A052386/b052386.txt">Table of n, a(n) for n = 0..500</a>
%H A052386 Peter D. Loly and Ian D. Cameron, <a href="https://arxiv.org/abs/2008.11020">Frierson's 1907 Parameterization of Compound Magic Squares Extended to Orders 3^L, L = 1, 2, 3, ..., with Information Entropy</a>, arXiv:2008.11020 [math.HO], 2020.
%H A052386 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).
%F A052386 a(n) = 9*a(n-1) + 9.
%F A052386 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
%F A052386 a(n) = 10*a(n-1)-9*a(n-2). G.f.: 9*x / ((x-1)*(9*x-1)). - _Colin Barker_, Sep 26 2013
%e A052386 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.
%t A052386 Table[9(9^n - 1)/8, {n, 0, 20}]
%t A052386 LinearRecurrence[{10,-9},{0,9},30] (* _Harvey P. Dale_, Mar 22 2019 *)
%o A052386 (Magma) [9*(9^n-1)/8: n in [0..20]]; // _Vincenzo Librandi_, Jul 04 2011
%o A052386 (PARI) a(n)=9^(n+1)\8 \\ _Charles R Greathouse IV_, Aug 25 2014
%Y A052386 Cf. A024101, A052379.
%Y A052386 Row n=9 of A228275.
%K A052386 easy,nonn,base
%O A052386 0,2
%A A052386 _Odimar Fabeny_, Mar 10 2000
%E A052386 More terms and revised description from _James Sellers_, Mar 13 2000
%E A052386 More terms and revised description from _Robert G. Wilson v_, Apr 14 2003
%E A052386 More terms from _Colin Barker_, Sep 26 2013