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A034967 Sum of digits of numbers between 0 and (10^n)-1. 12
0, 45, 900, 13500, 180000, 2250000, 27000000, 315000000, 3600000000, 40500000000, 450000000000, 4950000000000, 54000000000000, 585000000000000, 6300000000000000, 67500000000000000, 720000000000000000, 7650000000000000000, 81000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Edward J. Barbeau, Murray S. Klamkin & William O. J. Moser, Five Hundred Mathematical Challenges, Problem 284 at pp. 142-143 (1995).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = 45*n*10^(n-1).

a(n) = 20*a(n-1) - 100*a(n-2), a(0)=0, a(1)=45. - Harvey P. Dale, Oct 09 2011

G.f.: (45*x)/(10*x-1)^2. - Harvey P. Dale, Oct 09 2011

a(n) = (9*n*10^n)/2. - Harvey P. Dale, Apr 23 2018

MAPLE

seq(45*n*10^(n-1), n=0..30); # Robert Israel, Jun 29 2018

MATHEMATICA

Table[45n 10^(n-1), {n, 0, 20}] (* or *) LinearRecurrence[{20, -100}, {0, 45}, 21] (* From Harvey P. Dale, Oct 09 2011 *)

PROG

(PARI) a(n)=45*n*10^(n-1) \\ Charles R Greathouse IV, Oct 07 2015

(MAGMA) [45*n*10^(n-1): n in [0..30]]; // Vincenzo Librandi, Jun 30 2018

CROSSREFS

Cf. A037123.

Sequence in context: A024379 A134290 A078761 * A199352 A195466 A010961

Adjacent sequences:  A034964 A034965 A034966 * A034968 A034969 A034970

KEYWORD

nonn,easy,base

AUTHOR

Felice Russo

EXTENSIONS

More terms from James A. Sellers, Jan 19 2000

STATUS

approved

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Last modified February 26 03:09 EST 2020. Contains 332272 sequences. (Running on oeis4.)