A089906 Sum of digits of numbers between 0 and (4/9)*(10^n-1).

0, 10, 270, 4650, 66430, 864210, 10641990, 126419770, 1464197550, 16641975330, 186419753110, 2064197530890, 22641975308670, 246419753086450, 2664197530864230, 28641975308642010, 306419753086419790

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, A089907, A089908, A089909, A034967.

Formula

a(n) = s(4, 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) = (2*(-55*(-1+10^n)+9*(10+9*10^n)*n))/81. G.f.: 10*x*(12*x^2+5*x+1) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013