|
%I #31 Oct 28 2022 17:10:15
%S 0,45,900,13500,180000,2250000,27000000,315000000,3600000000,
%T 40500000000,450000000000,4950000000000,54000000000000,
%U 585000000000000,6300000000000000,67500000000000000,720000000000000000,7650000000000000000,81000000000000000000
%N Sum of digits of numbers between 0 and (10^n)-1.
%D Edward J. Barbeau, Murray S. Klamkin & William O. J. Moser, Five Hundred Mathematical Challenges, Problem 284 at pp. 142-143 (1995).
%H Vincenzo Librandi, <a href="/A034967/b034967.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20, -100).
%F a(n) = 45*n*10^(n-1).
%F a(n) = 20*a(n-1) - 100*a(n-2), a(0)=0, a(1)=45. - _Harvey P. Dale_, Oct 09 2011
%F G.f.: (45*x)/(10*x-1)^2. - _Harvey P. Dale_, Oct 09 2011
%F a(n) = (9*n*10^n)/2. - _Harvey P. Dale_, Apr 23 2018
%p seq(45*n*10^(n-1),n=0..30); # _Robert Israel_, Jun 29 2018
%t Table[45n 10^(n-1),{n,0,20}] (* or *) LinearRecurrence[{20,-100},{0,45},21] (* _Harvey P. Dale_, Oct 09 2011 *)
%o (PARI) a(n)=45*n*10^(n-1) \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Magma) [45*n*10^(n-1): n in [0..30]]; // _Vincenzo Librandi_, Jun 30 2018
%Y Cf. A037123.
%K nonn,easy,base
%O 0,2
%A _Felice Russo_
%E More terms from _James A. Sellers_, Jan 19 2000
|
