[seqfan] Re: G.f. for trees with degree at most 3
Richard Guy
rkg at cpsc.ucalgary.ca
Mon May 24 17:51:36 CEST 2010
Thankyou, Franklin, that puts paid to that. I mentally
added 576 to 322 and subtracted 128 and wishfully
got 780 instead of 870 to make a(12) divisible by
13. R.
On Mon, 24 May 2010, franktaw at netscape.net wrote:
> 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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