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A155671
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a(n) = 10^n - 9^n + 1^n.
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4
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1, 2, 20, 272, 3440, 40952, 468560, 5217032, 56953280, 612579512, 6513215600, 68618940392, 717570463520, 7458134171672, 77123207545040, 794108867905352, 8146979811148160, 83322818300333432, 849905364703000880
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of numbers from 1 to 10^n containing a 1 in their decimal expansion. - Charles R Greathouse IV, Mar 25 2009
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LINKS
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FORMULA
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G.f.: 1/(1-10*x)-1/(1-9*x)+1/(1-x).
E.g.f.: e^(10*x)-e^(9*x)+e^x.
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MATHEMATICA
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Table[10^n-9^n+1, {n, 0, 20}] (* or *) LinearRecurrence[{20, -109, 90}, {1, 2, 20}, 20] (* Harvey P. Dale, Nov 05 2017 *)
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PROG
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CROSSREFS
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Equals A016189 + 1. See that entry for more information.
Cf. A155654, A155655, A155656, A155657, A155658, A155659, A155660, A155661, A155662, A155663, A155664, A155665, A155666, A155667, A155668, A155669, A155670.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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