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A089903
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Sum of digits of numbers between 0 and (1/9)*(10^n-1).
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6
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0, 1, 48, 960, 14572, 195684, 2456796, 29567908, 345679020, 3956790132, 44567901244, 495679012356, 5456790123468, 59567901234580, 645679012345692, 6956790123456804, 74567901234567916, 795679012345679028
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = s(1, n-1) where s(a, k)=a*(k+1)+a^2*sum(i=0, k, i*10^(k-i))+sum(i=0, k, 5*a*(9*(k-i)+a- 1)*10^(k-i-1)).
a(n) = (-88*(-1+10^n)+9*(16+9*10^n)*n)/162. G.f.: x*(45*x^2+26*x+1) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013
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MATHEMATICA
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LinearRecurrence[{22, -141, 220, -100}, {0, 1, 48, 960}, 20] (* Harvey P. Dale, May 12 2023 *)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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