A089909 Sum of digits of numbers between 0 and (8/9)*(10^n-1).

0, 36, 748, 11460, 154572, 1945684, 23456796, 274567908, 3145679020, 35456790132, 394567901244, 4345679012356, 47456790123468, 514567901234580, 5545679012345692, 59456790123456804, 634567901234567916

Offset: 0

Author

Benoit Cloitre, Nov 14 2003

Keywords

• nonn
• base
• easy

Comments

From a suggestion of Yalcin Aktar

Links

• Index entries for linear recurrences with constant coefficients, signature (22,-141,220,-100).

Crossrefs

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

Formula

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)).

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