login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A095807 Number of integers from 0 to 10^n - 1 whose decimal digits include at least one 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
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
EXAMPLE
a(3)=181 because among 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
KEYWORD
nonn,easy,base
AUTHOR
Michael Taktikos, Aug 25 2004
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 4 16:59 EST 2024. Contains 370532 sequences. (Running on oeis4.)