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