The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A059482 a(0)=1, a(n) = a(n-1) + 8*10^(n-1). 9
 1, 9, 89, 889, 8889, 88889, 888889, 8888889, 88888889, 888888889, 8888888889, 88888888889, 888888888889, 8888888888889, 88888888888889, 888888888888889, 8888888888888889, 88888888888888889, 888888888888888889 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Related to the sum of Fibonacci-variants: Sum of the (Fibonacci numbers)/(10^n) = 0/(10^1) + 1/(10^2) + 1/(10^3) + 2/(10^4) + 3/(10^5) + 5/(10^6) + ... = 1/89. Sum of the (tribonacci numbers)/(10^(n+1)) = 1/889. Sum of the (tetranacci numbers)/(10^(n+2)) = 1/8889, etc. The denominators of those sums is the current sequence. The first one is of course 0.11111111111... = 1/9. - partially edited by Michel Marcus, Jan 27 2014 Let A be the Hessenberg matrix of the order n, defined by: A[1,j]=1, A[i,i]:=12, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=(-1)^(n-1)*charpoly(A,2). - Milan Janjic, Feb 21 2010 Except for the initial term, these are the 9-automorphic numbers ending in 9. - Eric M. Schmidt, Aug 17 2012 LINKS Harry J. Smith, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (11,-10). FORMULA a(n) = (10^n)*(1000/1125) + (1/9). a(n) = A002282(n) + 1 = (8*10^n + 1)/9. a(n) = 10*a(n-1) - 1 with n > 0, a(0)=1. - Vincenzo Librandi, Aug 07 2010 G.f.: -(2*x-1) / ((x-1)*(10*x-1)). - Colin Barker, Feb 02 2013 a(n) = 10^n - Sum_{i=0..n-1} 10^i for n > 0. - Bruno Berselli, Jun 20 2013 EXAMPLE a(3) = (10^3)*(1000/1125) + (1/9) = (8000/9) + (1/9) = 889. MATHEMATICA Table[(8*10^n+1)/9, {n, 0, 50}] (* G. C. Greubel, May 15 2017 *) PROG (PARI) { a=1/5; for (n = 0, 200, a+=8*10^(n - 1); write("b059482.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 27 2009 (Python) def a(n): return (8*10**n+1)//9 # Martin Gergov, Oct 20 2022 CROSSREFS Sequence in context: A015584 A072256 A138288 * A109002 A142991 A152267 Adjacent sequences: A059479 A059480 A059481 * A059483 A059484 A059485 KEYWORD nonn,easy AUTHOR Anton Joha, Feb 04 2001 EXTENSIONS More terms from Henry Bottomley, Feb 05 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 30 19:14 EST 2022. Contains 358453 sequences. (Running on oeis4.)