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A192937
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a(n) = 100*a(n-1) - (n-1) with a(1)=100.
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1
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100, 9999, 999898, 99989797, 9998979696, 999897969595, 99989796959494, 9998979695949393, 999897969594939292, 99989796959493929191, 9998979695949392919090, 999897969594939291908989
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OFFSET
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1,1
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LINKS
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FORMULA
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G.f.: x*(100-201*x+100*x^2)/((1-100*x)*(1-x)^2).
a(n) = (9800*100^n+99*n+1)/9801. (End)
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EXAMPLE
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For n=2: a(2)=100*a(1)-(2-1)=100*100-1=10000-1=9999.
For n=3: a(3)=100*a(2)-(3-1)=100*9999-2=999900-2=999898.
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MAPLE
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a[1]:=100; for n from 2 to 12 do a[n]:=100*a[n-1]-(n-1); end do;
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MATHEMATICA
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LinearRecurrence[{102, -201, 100}, {100, 9999, 999898}, 20] (* G. C. Greubel, Feb 06 2019 *)
RecurrenceTable[{a[1]==100, a[n]==100a[n-1]-n+1}, a, {n, 20}] (* Harvey P. Dale, May 17 2019 *)
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PROG
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(Magma) [n lt 2 select 100 else 100*Self(n-1)-n+1: n in [1..14]]; // Bruno Berselli, Aug 02 2011
(PARI) vector(20, n, (98*10^(2*n+2) +99*n +1)/9801) \\ G. C. Greubel, Feb 06 2019
(Sage) [(98*10^(2*n+2) +99*n +1)/9801 for n in (1..20)] # G. C. Greubel, Feb 06 2019
(GAP) List([1..20], n -> (98*10^(2*n+2) +99*n +1)/9801); # G. C. Greubel, Feb 06 2019
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CROSSREFS
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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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