

A059482


a(0)=1, a(n) = a(n1) + 8*10^(n1).


9



1, 9, 89, 889, 8889, 88889, 888889, 8888889, 88888889, 888888889, 8888888889, 88888888889, 888888888889, 8888888888889, 88888888888889, 888888888888889, 8888888888888889, 88888888888888889, 888888888888888889
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OFFSET

0,2


COMMENTS

Related to the sum of Fibonaccivariants: 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,i1]=1, and A[i,j]=0 otherwise. Then, for n>=1, a(n1)=(1)^(n1)*charpoly(A,2).  Milan Janjic, Feb 21 2010
Except for the initial term, these are the 9automorphic 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(n1)  1 with n > 0, a(0)=1.  Vincenzo Librandi, Aug 07 2010
G.f.: (2*x1) / ((x1)*(10*x1)).  Colin Barker, Feb 02 2013
a(n) = 10^n  Sum_{i=0..n1} 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



