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Search: id:A125858
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| A125858 |
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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. |
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+0
18
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| 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 999637120, 9980041600, 99381289600, 985729744000, 9726841354240, 95404977568000, 929690189228800, 8999055703648000, 86532737999167360, 826798452380099200
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Note that the first eight terms of the sequence are powers of 10.
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
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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
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EXAMPLE
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a(9)=999637120
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MAPLE
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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;
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MATHEMATICA
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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 (rgwv(AT)rgwv.com), 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 (rgwv(AT)rgwv.com), May 31 2009]
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CROSSREFS
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Cf. A125630.
Sequence in context: A135654 A029800 A100061 this_sequence A086067 A136873 A135655
Adjacent sequences: A125855 A125856 A125857 this_sequence A125859 A125860 A125861
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KEYWORD
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nonn,base
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AUTHOR
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Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), Feb 03 2007
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