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A033713
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Number of zeros in numbers 1 to 999..9 (n digits).
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4
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0, 9, 189, 2889, 38889, 488889, 5888889, 68888889, 788888889, 8888888889, 98888888889, 1088888888889, 11888888888889, 128888888888889, 1388888888888889, 14888888888888889, 158888888888888889
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also the first n places of 1, ..., n-digit numbers in the almost-natural numbers (A007376). - Erich Friedman (erich.friedman(AT)stetson.edu).
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REFERENCES
| M. Kraitchik, Mathematical Recreations. Dover, NY, 2nd ed., 1953, p. 49.
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FORMULA
| a(n) = (1/9)*((n-1)*(10^n)-n*10^(n-1)+1); g.f.: (9*x^2)/((1-x)(1-10x)^2) - Stephen G. Penrice (spenrice(AT)ets.org), Oct 01 2000
Sum 9i*10^(i-1), i=1..n.
a(1)=0, a(2)=9, a(3)=189, a(n)=21*a(n-1)-120*a(n-2)+100*a(n-3) [From Harvey P. Dale, Jan 24 2012]
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MATHEMATICA
| Table[ Sum[9i*10^(i - 1), {i, 1, n}], {n, 0, 16}]
LinearRecurrence[{21, -120, 100}, {0, 9, 189}, 30] (* From Harvey P. Dale, Jan 24 2012 *)
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CROSSREFS
| Cf. A033714.
Sequence in context: A196215 A196682 A124008 * A067422 A145240 A113564
Adjacent sequences: A033710 A033711 A033712 * A033714 A033715 A033716
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KEYWORD
| nonn,base,nice,easy
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AUTHOR
| Olivier Gorin (gorin(AT)roazhon.inra.fr)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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