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.

10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 999637120, 9980041600, 99381289600, 985729744000, 9726841354240, 95404977568000, 929690189228800, 8999055703648000, 86532737999167360, 826798452380099200, 7852626768025993600

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