[seqfan] Re: G.f. for trees with degree at most 3
Charles Greathouse
charles.greathouse at case.edu
Mon May 24 03:24:53 CEST 2010
My Pari script reports
(21:23) findrec([1, 1, 3, 16, 120, 1170, 14070, 201600, 3356640,
63730800, 1359666000, 32212857600, 839350512000])
Cannot be described by a homogeneous linear recurrence relation with 6
or fewer coefficients.
%1 = 0
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
On Sun, May 23, 2010 at 6:35 PM, Richard Guy <rkg at cpsc.ucalgary.ca> wrote:
> 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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