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

[Richard Guy]

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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