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.
%I A078427 #30 Mar 23 2024 07:24:45
%S A078427 46,901,13501,180001,2250001,27000001,315000001,3600000001,
%T A078427 40500000001,450000000001,4950000000001,54000000000001,
%U A078427 585000000000001,6300000000000001,67500000000000001,720000000000000001,7650000000000000001,81000000000000000001
%N A078427 Sum of all the decimal digits of numbers from 1 to 10^n.
%D A078427 E. J. Barbeau et al., Five Hundred Mathematical Challenges, Problem 284. pp. 25; 142-143, MAA Washington DC, 1995.
%H A078427 Vincenzo Librandi, <a href="/A078427/b078427.txt">Table of n, a(n) for n = 1..200</a>
%H A078427 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-120,100).
%F A078427 a(n) = (45*n)*10^(n-1)+1.
%F A078427 a(n) = 45*A053541(n)+1. - _Lekraj Beedassy_, Sep 16 2006
%F A078427 a(n) = 21*a(n-1)-120*a(n-2)+100*a(n-3). - _Colin Barker_, May 23 2014
%F A078427 G.f.: -x*(100*x^2-65*x+46) / ((x-1)*(10*x-1)^2). - _Colin Barker_, May 23 2014
%e A078427 a(2)=901 because sum of all the digits of numbers from 1 to 10^2 is 901.
%t A078427 LinearRecurrence[{21,-120,100},{46,901,13501},20] (* _Harvey P. Dale_, Nov 24 2016 *)
%o A078427 (Magma) [(45*n)*10^(n-1)+1: n in [1..30]]; // _Vincenzo Librandi_, Jun 06 2011
%o A078427 (PARI) Vec(-x*(100*x^2-65*x+46)/((x-1)*(10*x-1)^2) + O(x^100)) \\ _Colin Barker_, May 23 2014
%Y A078427 Cf. A053541, A072290.
%K A078427 nonn,base,easy
%O A078427 1,1
%A A078427 _Shyam Sunder Gupta_, Dec 29 2002
%E A078427 Edited by _Charles R Greathouse IV_, Aug 02 2010
%E A078427 More terms from _Colin Barker_, May 23 2014