A087330 Sum of all digits of all integers less than or equal to 555...55 (with n 5's) in base 10.

0, 15, 370, 6150, 86430, 1114210, 13641990, 161419770, 1864197550, 21141975330, 236419753110, 2614197530890, 28641975308670, 311419753086450, 3364197530864230, 36141975308642010, 386419753086419790

Offset: 0

Author

Benoit Cloitre, Oct 20 2003

Keywords

• base
• nonn
• easy

Comments

From a suggestion of Yalcin Aktar

Examples

			a(1)=15 since numbers less than or equal to 5 are 1,2,3,4,5 and the sum of digits is 1+2+3+4+5=15.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (22,-141,220,-100).

Programs

Mathematica

LinearRecurrence[{22,-141,220,-100},{0,15,370,6150},20] (* Harvey P. Dale, Aug 01 2016 *)

Formula

a(n) = 20/9*n-110/81*10^n+110/81+5/2*n*10^n (formula from B. Greco).

G.f.: 5*x*(25*x^2+8*x+3) / ((x-1)^2*(10*x-1)^2). - Colin Barker, Jun 14 2013