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A125858 a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks at least one of digits 1,2,3,4,5,6,7,8,9. 19
10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 999637120, 9980041600, 99381289600, 985729744000, 9726841354240, 95404977568000, 929690189228800, 8999055703648000, 86532737999167360, 826798452380099200, 7852626768025993600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Note that the first eight terms of the sequence are powers of 10.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index entries for linear recurrences with constant coefficients, signature (45,-870,9450,-63273,269325,-723680,1172700,-1026576,362880).

FORMULA

a(n) = 9*9^n-36*8^n+84*7^n-126*6^n+126*5^n-84*4^n+36*3^n-9*2^n+1.

MAPLE

f:=n->9*9^n-36*8^n+84*7^n-126*6^n+126*5^n-84*4^n+36*3^n-9*2^n+1;

MATHEMATICA

f[n_] := (9*9^n - 36*8^n + 84*7^n - 126*6^n + 126*5^n - 84*4^n + 36*3^n - 9*2^n + 1); Array[f, 18] (* Robert G. Wilson v, May 31 2009 *)

(* or *) f[n_] := Sum[ -(-1)^k*Binomial[9, k] (10 - k)^n, {k, 9}]; Array[f, 18] (* Robert G. Wilson v, May 31 2009 *)

PROG

(PARI) vector(100, n, 9*9^n-36*8^n+84*7^n-126*6^n+126*5^n-84*4^n+36*3^n-9*2^n+1) \\ Colin Barker, Feb 23 2015

CROSSREFS

Cf. A125630.

Sequence in context: A168070 A263019 A100061 * A086067 A348783 A260522

Adjacent sequences:  A125855 A125856 A125857 * A125859 A125860 A125861

KEYWORD

nonn,base,easy

AUTHOR

Aleksandar M. Janjic and Milan Janjic, Feb 03 2007

EXTENSIONS

Incorrect g.f. removed by Georg Fischer, May 15 2019

STATUS

approved

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Last modified May 21 03:13 EDT 2022. Contains 353886 sequences. (Running on oeis4.)