A089905 Sum of digits of numbers between 0 and (3/9)*(10^n-1).

0, 6, 183, 3285, 47787, 627789, 7777791, 92777793, 1077777795, 12277777797, 137777777799, 1527777777801, 16777777777803, 182777777777805, 1977777777777807, 21277777777777809, 227777777777777811

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, A089906, A087330, A089906, A089907, A089908, A034967.

Programs

Mathematica

LinearRecurrence[{22,-141,220,-100},{0,6,183,3285},20] (* Harvey P. Dale, Apr 19 2013 *)

Formula

a(n) = s(3, 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) = 22*a(n-1)-141*a(n-2)+220*a(n-3)-100*a(n-4). - T. D. Noe, Nov 08 2006

a(n) = (-11/9*(-1+10^n)+1/2*(4+3*10^n)*n). G.f.: 3*x*(5*x+1)*(7*x+2) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013

Extensions

Corrected by T. D. Noe, Nov 08 2006