%I #20 Mar 26 2024 14:46:08
%S 0,3,109,2055,30501,404947,5049393,60493839,704938285,8049382731,
%T 90493827177,1004938271623,11049382716069,120493827160515,
%U 1304938271604961,14049382716049407,150493827160493853
%N Sum of digits of numbers between 0 and (2/9)*(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(2, 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) = (-77*(-1+10^n)+9*(14+9*10^n)*n)/81. G.f.: x*(80*x^2+43*x+3) / ((x-1)^2*(10*x-1)^2). - _Colin Barker_, Jun 14 2013
%Y Cf. A089903, A089905, A089906, A087330, A089907, A089908, A089909, A034967.
%K nonn,base,easy
%O 0,2
%A _Benoit Cloitre_, Nov 14 2003
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