A095807 Number of integers from 0 to 10^n - 1 whose decimal digits include at least one 0.

1, 10, 181, 2620, 33571, 402130, 4619161, 51572440, 564151951, 6077367550, 64696307941, 682266771460, 7140400943131, 74263608488170, 768372476393521, 7915352287541680, 81238170587875111

Offset: 1

Author

Michael Taktikos, Aug 25 2004

Keywords

• nonn
• easy
• base

Examples

			a(3)=181 because among the integers from 0 to 999 there are 181 numbers which contain at least 1 zero.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (20,-109,90).

Crossrefs

Cf. A016189.

Programs

Magma

[10^n + 9/8 - 9^(1+n)/8: n in [1..20]]; // Vincenzo Librandi, Aug 14 2013

Mathematica

LinearRecurrence[{20,-109,90},{1,10,181},20] (* or *) Rest[ CoefficientList[ Series[(1-19x+99x^2)/((1-x)(1-10x)(1-9x)),{x,0,20}], x]] (* Harvey P. Dale, Jun 20 2015 *)

PARI

a(n) = 10^n + 9/8 - 9^(1+n)/8; \\ Michel Marcus, Aug 13 2013

Formula

a(n) = 10^n + 9/8 - 9^(1+n)/8.

G.f.: (1-19*x+99*x^2)/((1-x)*(1-10*x)*(1-9*x)). - Vincenzo Librandi, Aug 14 2013

a(n) = 20*a(n-1) - 109*a(n-2) + 90*a(n-3); a(0)=1, a(1)=10, a(2)=181. - Harvey P. Dale, Jun 20 2015

Limit_{n->oo} a(n+1)/a(n) = 10. - Bernard Schott, Feb 28 2023