A006906 question

Paul D. Hanna pauldhanna at juno.com
Sun Aug 19 20:56:35 CEST 2007

Dean (and Seqfnas), 
     Good work.  Yet there may yet be a limit here that does exist.  
Is it not accurate to state: 
(*) the limit of a(n+3)/a(n) exists and is equal to 3. 
This can still be true and the limit of (*) unique 
even though a(n+1)/a(n) takes on 3 different values -  
as long as the product of these 3 limit points equals 3. 
Does that (*) check out as true in your analysis? 
Empirically, in my trials, (*) seems to hold very well. 
> > For A006906, could a(n+1)/a(n) be approaching a limit?
> > Like maybe 3^(1/3)?
> The limit does not exist.  The generating function for a(n) is
> Because these 3 values are different, the sequence of ratios 
> a(n+1)/a(n) has
> 3 different limit points, which differ slightly from 3^(1/3).

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