OFFSET
1,3
COMMENTS
This is analogous to the closed form of the formula for the n-th Fibonacci number. Even before truncation, these numbers are rational and the decimal part always ends in 5. For x=(sqrt(6)+1)/2, a(n)/a(n-1) -> x.
FORMULA
The general form of x is (sqrt(r)+1)/2, r=1,2,3..
a(n) = floor(b(n)/2^n) where b(n) = 2*A002532(n)+2^(n-1). - R. J. Mathar, Sep 10 2016
PROG
(PARI) g(n, r) = for(m=1, n, print1(fib(m, r)", ")) fib(n, r) = x=(sqrt(r)+1)/2; floor((x^n-(1-x)^n)/sqrt(r)+.5)
CROSSREFS
KEYWORD
nonn
AUTHOR
Cino Hilliard, Apr 01 2008
EXTENSIONS
Definition corrected by Frederic van der Plancke (fplancke(AT)hotmail.com), May 08 2009
STATUS
approved