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A078427
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Sum of all the decimal digits of numbers from 1 to 10^n.
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3
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46, 901, 13501, 180001, 2250001, 27000001, 315000001, 3600000001, 40500000001, 450000000001, 4950000000001, 54000000000001, 585000000000001, 6300000000000001, 67500000000000001, 720000000000000001, 7650000000000000001, 81000000000000000001
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OFFSET
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1,1
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REFERENCES
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E. J. Barbeau et al., Five Hundred Mathematical Challenges, Problem 284. pp. 25; 142-143, MAA Washington DC, 1995.
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LINKS
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FORMULA
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a(n) = (45*n)*10^(n-1)+1.
a(n) = 21*a(n-1)-120*a(n-2)+100*a(n-3). - Colin Barker, May 23 2014
G.f.: -x*(100*x^2-65*x+46) / ((x-1)*(10*x-1)^2). - Colin Barker, May 23 2014
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EXAMPLE
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a(2)=901 because sum of all the digits of numbers from 1 to 10^2 is 901.
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MATHEMATICA
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LinearRecurrence[{21, -120, 100}, {46, 901, 13501}, 20] (* Harvey P. Dale, Nov 24 2016 *)
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PROG
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(PARI) Vec(-x*(100*x^2-65*x+46)/((x-1)*(10*x-1)^2) + O(x^100)) \\ Colin Barker, May 23 2014
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CROSSREFS
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KEYWORD
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nonn,base,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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