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A089903
Sum of digits of numbers between 0 and (1/9)*(10^n-1).
6
0, 1, 48, 960, 14572, 195684, 2456796, 29567908, 345679020, 3956790132, 44567901244, 495679012356, 5456790123468, 59567901234580, 645679012345692, 6956790123456804, 74567901234567916, 795679012345679028
OFFSET
0,3
COMMENTS
From a suggestion of Yalcin Aktar
FORMULA
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
MATHEMATICA
LinearRecurrence[{22, -141, 220, -100}, {0, 1, 48, 960}, 20] (* Harvey P. Dale, May 12 2023 *)
KEYWORD
nonn,base,easy
AUTHOR
Benoit Cloitre, Nov 14 2003
STATUS
approved