A089907 Sum of digits of numbers between 0 and (6/9)*(10^n-1).

0, 21, 483, 7785, 107787, 1377789, 16777791, 197777793, 2277777795, 25777777797, 287777777799, 3177777777801, 34777777777803, 377777777777805, 4077777777777807, 43777777777777809, 467777777777777811

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, A089908, A089909, A034967.

Programs

Mathematica

LinearRecurrence[{22,-141,220,-100},{0,21,483,7785},20] (* Harvey P. Dale, Aug 22 2022 *)

Formula

a(n) = s(6, 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) = (-11/9*(-1+10^n)+(2+3*10^n)*n). G.f.: 3*x*(40*x^2+7*x+7) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013