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A094797
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Number of times 1 is used in writing out all numbers 1 through 10^n.
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0
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1, 2, 21, 301, 4001, 50001, 600001, 7000001, 80000001, 900000001, 10000000001, 110000000001, 1200000000001, 13000000000001, 140000000000001, 1500000000000001, 16000000000000001, 170000000000000001, 1800000000000000001, 19000000000000000001
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 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.: -(99*x^2-19*x+1) / ((x-1)*(10*x-1)^2). - Colin Barker, May 23 2014
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MATHEMATICA
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LinearRecurrence[{21, -120, 100}, {1, 2, 21}, 20] (* Harvey P. Dale, Sep 07 2022 *)
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PROG
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(PARI) Vec(-(99*x^2-19*x+1)/((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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base,nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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