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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. 17
 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 999637120, 9980041600, 99381289600, 985729744000, 9726841354240, 95404977568000, 929690189228800, 8999055703648000, 86532737999167360, 826798452380099200 (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 Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets 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 EXAMPLE a(9)=999637120 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] [From Robert G. Wilson v, May 31 2009] (* or *) f[n_] := Sum[ -(-1)^k*Binomial[9, k] (10 - k)^n, {k, 9}]; Array[f, 18] [From Robert G. Wilson v, May 31 2009] CROSSREFS Cf. A125630. Sequence in context: A029800 A168070 A100061 * A086067 A136873 A135655 Adjacent sequences:  A125855 A125856 A125857 * A125859 A125860 A125861 KEYWORD nonn,base AUTHOR Aleksandar M. Janjic and Milan Janjic, Feb 03 2007 STATUS approved

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