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 A033713 Number of zeros in numbers 1 to 999..9 (n digits). 8
 0, 9, 189, 2889, 38889, 488889, 5888889, 68888889, 788888889, 8888888889, 98888888889, 1088888888889, 11888888888889, 128888888888889, 1388888888888889, 14888888888888889, 158888888888888889 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also the first n places of 1, ..., n-digit numbers in the almost-natural numbers (A007376). - Erich Friedman. REFERENCES F. Calogero, Cool irrational numbers and their rather cool rational approximations, Math. Intell. 25 (4) (2003) 72-76 doi:10.1007/BF02984865 M. Kraitchik, Mathematical Recreations. Dover, NY, 2nd ed., 1953, p. 49. LINKS Index entries for linear recurrences with constant coefficients, signature (21,-120,100). 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] MATHEMATICA Table[ Sum[9i*10^(i - 1), {i, 1, n}], {n, 0, 16}] LinearRecurrence[{21, -120, 100}, {0, 9, 189}, 30] (* Harvey P. Dale, Jan 24 2012 *) PROG (PARI) a(n)=((n-1)*(10^n)-n*10^(n-1)+1)/9 \\ Charles R Greathouse IV, Feb 19 2017 CROSSREFS Cf. A033714. Sequence in context: A196215 A196682 A124008 * A067422 A249932 A278751 Adjacent sequences:  A033710 A033711 A033712 * A033714 A033715 A033716 KEYWORD nonn,base,nice,easy AUTHOR Olivier Gorin (gorin(AT)roazhon.inra.fr) EXTENSIONS More terms from Erich Friedman. STATUS approved

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Last modified February 25 07:33 EST 2020. Contains 332221 sequences. (Running on oeis4.)