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%I #24 Mar 15 2023 12:39:46
%S 0,6,183,3285,47787,627789,7777791,92777793,1077777795,12277777797,
%T 137777777799,1527777777801,16777777777803,182777777777805,
%U 1977777777777807,21277777777777809,227777777777777811
%N Sum of digits of numbers between 0 and (3/9)*(10^n-1).
%C From a suggestion of _Yalcin Aktar_
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (22,-141,220,-100).
%F a(n) = s(3, 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))
%F a(n) = 22*a(n-1)-141*a(n-2)+220*a(n-3)-100*a(n-4). - _T. D. Noe_, Nov 08 2006
%F a(n) = (-11/9*(-1+10^n)+1/2*(4+3*10^n)*n). G.f.: 3*x*(5*x+1)*(7*x+2) / ((x-1)^2*(10*x-1)^2). - _Colin Barker_, Jun 14 2013
%t LinearRecurrence[{22,-141,220,-100},{0,6,183,3285},20] (* _Harvey P. Dale_, Apr 19 2013 *)
%Y Cf. A089903, A089904, A089906, A087330, A089906, A089907, A089908, A034967.
%K nonn,base,easy
%O 0,2
%A _Benoit Cloitre_, Nov 14 2003
%E Corrected by _T. D. Noe_, Nov 08 2006
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