|
| |
|
|
A059482
|
|
a(0)=1, a(n)=a(n-1)+8*10^(n-1).
|
|
7
| |
|
|
1, 9, 89, 889, 8889, 88889, 888889, 8888889, 88888889, 888888889, 8888888889, 88888888889, 888888888889, 8888888888889, 88888888888889, 888888888888889, 8888888888888889, 88888888888888889, 888888888888888889
(list; graph; refs; listen; history; 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 dominator-sequence of those sums is A059482. The first one is of course 0.11111111111 = 1/9.
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). [From Milan R. Janjic (agnus(AT)blic.net), Feb 21 2010]
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,200
|
|
|
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 a(0)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
|
|
|
EXAMPLE
| a(3)=(10^3)*(1000/1125)+(1/9)=(8000/9)+(1/9)=889.
a(1)=10*1-1=9; a(2)=10*9-1=89; a(3)=10*89-1=889 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
|
|
|
PROG
| (PARI) { a=1/5; for (n = 0, 200, a+=8*10^(n - 1); write("b059482.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 27 2009]
|
|
|
CROSSREFS
| Sequence in context: A015584 A072256 A138288 * A109002 A142991 A152267
Adjacent sequences: A059479 A059480 A059481 * A059483 A059484 A059485
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| A. Joha (A.S.J.R.Joha(AT)student.tbm.tudelft.nl), Feb 04 2001
|
|
|
EXTENSIONS
| More terms from Henry Bottomley (se16(AT)btinternet.com), Feb 05 2001
|
| |
|
|
