Re: Lucas/Fibonacci bisections
From: Elisabeth E. Korelines (esme_at_uboot.at)
Date: 08/29/04
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Date: 29 Aug 2004 10:43:18 -0700
crowdog@o2online.de (Dement) wrote in message news:<200408272014.i7RKEFH26803@proapp.mathforum.org>...
> I realized that the sequence of ratios a(n+1)/a(n) from the sequence
> http://www.research.att.com/projects/OEIS?Anum=A097512
> appears to approach the golden ratio phi + 1 = (3+sqrt(5))/2
>
> This happens for Lucas(2n) and Fib(2n) as well. Might this
> suggest that another (possibly unknown) sequence "X" exists
> such that X(2n) = a(n)?
>
Yes, X is http://www.research.att.com/projects/OEIS?Anum=A022133.
But this doesn't follow from the asymptotic ratio alone, you need the
fact that the recurrence is the same.
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