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A053541 a(n) = n*10^(n-1). 12

%I

%S 1,20,300,4000,50000,600000,7000000,80000000,900000000,10000000000,

%T 110000000000,1200000000000,13000000000000,140000000000000,

%U 1500000000000000,16000000000000000,170000000000000000

%N a(n) = n*10^(n-1).

%C This sequence gives the number of 1's (or any other digit) required to write all integers of n or fewer digits. It is thus A094798 for n=9, 99, 999, .... Another formula: a(n) = 10*a(n-1) + 10*(n-1) a(n) = Sum_{k=1...n} k*binomial(n,k)*9^(n-k) - Jason D. W. Taff (jtaff(AT)jburroughs.org), Dec 05 2004

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

%H Vincenzo Librandi, <a href="/A053541/b053541.txt">Table of n, a(n) for n = 1..100</a>

%H F. Ellermann, <a href="/A001792/a001792.txt">Illustration of binomial transforms</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100).

%F a(n) = 20*a(n-1) - 100*a(n-2), with a(0)=0, a(1)=1, a(2)=20.

%F From _G. C. Greubel_, May 16 2019: (Start)

%F G.f.: x/(1-10*x)^2.

%F E.g.f.: x*exp(10*x). (End)

%t f[n_]:=n*10^(n-1);f[Range[40]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011*)

%o (MAGMA) [n*10^(n-1): n in [1..30]]; // _Vincenzo Librandi_, Jun 06 2011

%o (PARI) a(n)=n*10^(n-1) \\ _Charles R Greathouse IV_, Dec 05 2011

%o (Sage) [n*10^(n-1) for n in (1..20)] # _G. C. Greubel_, May 16 2019

%o (GAP) List([1..20], n-> n*10^(n-1)) # _G. C. Greubel_, May 16 2019

%Y Cf. A001787, A053464, A053469, A094798, A038303.

%K easy,nonn

%O 1,2

%A _Barry E. Williams_, Jan 15 2000

%E Offset changed from 0 to 1 by _Vincenzo Librandi_, Jun 06 2011

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Last modified October 14 16:40 EDT 2019. Contains 328022 sequences. (Running on oeis4.)