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

Offset: 0

Author

Felice Russo

Keywords

• nonn
• easy
• base

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).

Crossrefs

Cf. A037123.

Programs

Magma

[45*n*10^(n-1): n in [0..30]]; // Vincenzo Librandi, Jun 30 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] (* Harvey P. Dale, Oct 09 2011 *)

PARI

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

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

Extensions

More terms from James Sellers, Jan 19 2000