OFFSET
1,2
COMMENTS
Also the first n places of 1, ..., n-digit numbers in the almost-natural numbers (A007376). - Erich Friedman.
a(n+1) is also the total number of digits in numbers from 1 through 999..9 (n digits). - Jianing Song, Apr 17 2022
REFERENCES
M. Kraitchik, Mathematical Recreations. Dover, NY, 2nd ed., 1953, p. 49.
LINKS
FORMULA
From Stephen G Penrice, Oct 01 2000: (Start)
a(n) = (1/9)*((n-1)*(10^n)-n*10^(n-1)+1).
G.f.: (9*x^2)/((1-x)(1-10x)^2). (End)
a(n) = Sum_{i=1..n} 9*i*10^(i-1).
a(1)=0, a(2)=9, a(3)=189, a(n)=21*a(n-1)-120*a(n-2)+100*a(n-3). - Harvey P. Dale, Jan 24 2012
a(n+1) = A058183(10^n-1) for n >= 1. - Jianing Song, Apr 17 2022
E.g.f.: exp(x)*(1 + exp(9*x)*(9*x - 1))/9. - Stefano Spezia, Sep 13 2023
MATHEMATICA
Table[ Sum[9i*10^(i - 1), {i, 1, n}], {n, 0, 16}]
LinearRecurrence[{21, -120, 100}, {0, 9, 189}, 30] (* Harvey P. Dale, Jan 24 2012 *)
PROG
(PARI) a(n)=((n-1)*(10^n)-n*10^(n-1)+1)/9 \\ Charles R Greathouse IV, Feb 19 2017
CROSSREFS
KEYWORD
nonn,base,nice,easy
AUTHOR
Olivier Gorin (gorin(AT)roazhon.inra.fr)
EXTENSIONS
More terms from Erich Friedman.
a(18)-a(21) from Stefano Spezia, Sep 13 2023
STATUS
approved