A034967 Sum of digits of numbers between 0 and (10^n)-1.

0, 45, 900, 13500, 180000, 2250000, 27000000, 315000000, 3600000000, 40500000000, 450000000000, 4950000000000, 54000000000000, 585000000000000, 6300000000000000, 67500000000000000, 720000000000000000, 7650000000000000000, 81000000000000000000, 855000000000000000000

Offset

0,2

References

Edward J. Barbeau, Murray S. Klamkin, and 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).

From Harvey P. Dale, Oct 09 2011: (Start)

a(n) = 20*a(n-1) - 100*a(n-2), a(0)=0, a(1)=45.

G.f.: 45*x/(10*x-1)^2. (End)

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

From Elmo R. Oliveira, Nov 20 2025: (Start)

E.g.f.: 45*x*exp(10*x).

a(n) = 45*A053541(n). (End)

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] (* 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, A053541.

Sequence in context: A359933 A341573 A078761 * A199352 A195466 A010961

Adjacent sequences: A034964 A034965 A034966 * A034968 A034969 A034970

Keyword

nonn,easy,base

Author

Felice Russo

Extensions

More terms from James Sellers, Jan 19 2000

Status

approved