[seqfan] Re: G.f. for trees with degree at most 3

[franktaw at netscape.net]

It's not a divisibility sequence. I assume you meant the right-shifted 
sequence; as it is,a(3) = 16 does not divide a(6) = 14070.  However, 
the right-shifted sequence is also not a divisibility sequence; for it, 
a(6) = 1170 does not divide a(12) = 32212857600.

Franklin T. Adams-Watters

-----Original Message-----
From: Richard Guy <rkg at cpsc.ucalgary.ca>

It looks as though it is a divisibility sequence.  Could 
someone check if it satisfies a linear recurrence of order 
6 or less?  (or more, but that would be very tentative)  R. 
 
On Sun, 23 May 2010, franktaw at netscape.net wrote: 
 
> I asked the author of this sequence for clarification, but got no > 
response. Maybe somebody here can figure out what is going on. 
> 
> http://www.research.att.com/~njas/sequences/A003692  
>   
> For this sequence, a generating function is given: 
> 
> (1-x)(2-x-x^2) - (2-x+x^2)\sqrt{1-2x-x^2} \over 3 x^3.  
>   
> I'm not sure if this is supposed to be  
>   
> (1-x)*(2-x-x^2)-(2-x-x^2)*sqrt(1-2*x-x^2)/(3*x^3)  
>   
> or  
>   
> ((1-x)*(2-x-x^2)-(2-x-x^2)*sqrt(1-2*x-x^2))/(3*x^3),  
>   
> but either one produces a series that includes terms with negative > 
exponents; and in neither case there is any apparent relationship to > 
this sequence. So what is the correct g.f.?  
>   
> Franklin T. Adams-Watters  
> 
> > 
> 
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> 
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