cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A034967 #32 Jul 02 2025 16:01:56
%S A034967 0,45,900,13500,180000,2250000,27000000,315000000,3600000000,
%T A034967 40500000000,450000000000,4950000000000,54000000000000,
%U A034967 585000000000000,6300000000000000,67500000000000000,720000000000000000,7650000000000000000,81000000000000000000
%N A034967 Sum of digits of numbers between 0 and (10^n)-1.
%D A034967 Edward J. Barbeau, Murray S. Klamkin & William O. J. Moser, Five Hundred Mathematical Challenges, Problem 284 at pp. 142-143 (1995).
%H A034967 Vincenzo Librandi, <a href="/A034967/b034967.txt">Table of n, a(n) for n = 0..1000</a>
%H A034967 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20, -100).
%F A034967 a(n) = 45*n*10^(n-1).
%F A034967 a(n) = 20*a(n-1) - 100*a(n-2), a(0)=0, a(1)=45. - _Harvey P. Dale_, Oct 09 2011
%F A034967 G.f.: (45*x)/(10*x-1)^2. - _Harvey P. Dale_, Oct 09 2011
%F A034967 a(n) = (9*n*10^n)/2. - _Harvey P. Dale_, Apr 23 2018
%p A034967 seq(45*n*10^(n-1),n=0..30); # _Robert Israel_, Jun 29 2018
%t A034967 Table[45n 10^(n-1),{n,0,20}] (* or *) LinearRecurrence[{20,-100},{0,45},21] (* _Harvey P. Dale_, Oct 09 2011 *)
%o A034967 (PARI) a(n)=45*n*10^(n-1) \\ _Charles R Greathouse IV_, Oct 07 2015
%o A034967 (Magma) [45*n*10^(n-1): n in [0..30]]; // _Vincenzo Librandi_, Jun 30 2018
%Y A034967 Cf. A037123.
%K A034967 nonn,easy,base
%O A034967 0,2
%A A034967 _Felice Russo_
%E A034967 More terms from _James Sellers_, Jan 19 2000