A089904 Sum of digits of numbers between 0 and (2/9)*(10^n-1).

0, 3, 109, 2055, 30501, 404947, 5049393, 60493839, 704938285, 8049382731, 90493827177, 1004938271623, 11049382716069, 120493827160515, 1304938271604961, 14049382716049407, 150493827160493853

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, A089905, A089906, A087330, A089907, A089908, A089909, A034967.

Formula

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)).

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