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A095807 Number of integers from 0 to 10^n-1 which contain at least one decimal digit = 0. 1
1, 10, 181, 2620, 33571, 402130, 4619161, 51572440, 564151951, 6077367550, 64696307941, 682266771460, 7140400943131, 74263608488170, 768372476393521, 7915352287541680, 81238170587875111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (20,-109,90).

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

EXAMPLE

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

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 *)

PROG

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

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

CROSSREFS

Cf. A016189.

Sequence in context: A030048 A318796 A054918 * A064092 A171513 A240405

Adjacent sequences:  A095804 A095805 A095806 * A095808 A095809 A095810

KEYWORD

nonn,easy,base

AUTHOR

Michael Taktikos, Aug 25 2004

STATUS

approved

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Last modified October 18 16:12 EDT 2018. Contains 316323 sequences. (Running on oeis4.)