%I #20 Mar 26 2024 14:45:52

%S 0,36,748,11460,154572,1945684,23456796,274567908,3145679020,

%T 35456790132,394567901244,4345679012356,47456790123468,

%U 514567901234580,5545679012345692,59456790123456804,634567901234567916

%N Sum of digits of numbers between 0 and (8/9)*(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(8, 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) = (4*(-11*(-1+10^n)+9*(2+9*10^n)*n))/81. G.f.: 4*x*(20*x^2-11*x+9) / ((x-1)^2*(10*x-1)^2). - _Colin Barker_, Jun 14 2013

%Y Cf. A089903, A089904, A089905, A087330, A089906, A089907, A089908, A034967.

%K nonn,base,easy

%O 0,2

%A _Benoit Cloitre_, Nov 14 2003