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A053541 a(n) = n*10^(n-1). 12
1, 20, 300, 4000, 50000, 600000, 7000000, 80000000, 900000000, 10000000000, 110000000000, 1200000000000, 13000000000000, 140000000000000, 1500000000000000, 16000000000000000, 170000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

REFERENCES

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

F. Ellermann, Illustration of binomial transforms

Index entries for linear recurrences with constant coefficients, signature (20,-100).

FORMULA

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

From G. C. Greubel, May 16 2019: (Start)

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

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

MATHEMATICA

f[n_]:=n*10^(n-1); f[Range[40]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011*)

PROG

(MAGMA) [n*10^(n-1): n in [1..30]]; // Vincenzo Librandi, Jun 06 2011

(PARI) a(n)=n*10^(n-1) \\ Charles R Greathouse IV, Dec 05 2011

(Sage) [n*10^(n-1) for n in (1..20)] # G. C. Greubel, May 16 2019

(GAP) List([1..20], n-> n*10^(n-1)) # G. C. Greubel, May 16 2019

CROSSREFS

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

Sequence in context: A138794 A077758 A202270 * A004345 A001755 A016190

Adjacent sequences:  A053538 A053539 A053540 * A053542 A053543 A053544

KEYWORD

easy,nonn,changed

AUTHOR

Barry E. Williams, Jan 15 2000

EXTENSIONS

Offset changed from 0 to 1 by Vincenzo Librandi, Jun 06 2011

STATUS

approved

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Last modified May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)