A089903 Sum of digits of numbers between 0 and (1/9)*(10^n-1).

0, 1, 48, 960, 14572, 195684, 2456796, 29567908, 345679020, 3956790132, 44567901244, 495679012356, 5456790123468, 59567901234580, 645679012345692, 6956790123456804, 74567901234567916, 795679012345679028

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. A089904, A089905, A089906, A087330, A089907, A089908, A089909, A034967.

Programs

Mathematica

LinearRecurrence[{22,-141,220,-100},{0,1,48,960},20] (* Harvey P. Dale, May 12 2023 *)

Formula

a(n) = s(1, 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) = (-88*(-1+10^n)+9*(16+9*10^n)*n)/162. G.f.: x*(45*x^2+26*x+1) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013