[seqfan] Re: My tool for exploring sequences

Alexander Povolotsky apovolot at gmail.com
Sun Dec 20 00:28:54 CET 2015


> (exp(-log(x^3+x^2+3*x-1)/2+5*log(3*x-1)-log(x-1)/2))/ (1-3*x)^5

could be further reduced to
(-1 + 3 x)^5/((1 - 3 x)^5 Sqrt[-1 + x] Sqrt[-1 + 3 x + x^2 + x^3])
and indeed
taylor (-1 + 3 x)^5/((1 - 3 x)^5 Sqrt[-1 + x] Sqrt[-1 + 3 x + x^2 + x^3])
yields coefficients, empirically coinciding with terms of A108626

> On Dec 19, 2015, at 4:14 PM, Thomas Baruchel <baruchel at gmx.com> wrote:
> 
>> On Sat, 19 Dec 2015, Alexander Povolotsky wrote:
>> Hi Dear Thomas,
>> 
>> Could You share results, which you have obtained using your tool?
> 
> Hi, I am going to leave my home for the holidays, but very quickly, I
> take a sequence I contributed some months ago, which is: A108626
> (I didn't try many sequences for the current reply; I really picked this
> one at first by hoping it could give something interesting).
> 
> I type:
> 
> java -jar target/oeis-deconvolution2-1.0.0-standalone.jar -d \
> ../oeis-deconvolution/stripped.gz "1, 2, 5, 14, 41, 124, 383, 1200, \
> 3799, 12122, 38919, 125578, 406865, 1322772, 4313155, 14099524"
> 
> Among the printed results, one seems interesting because it has a lower
> norm than other results:
> 
>> Deconvolution with A036217:
>> is (1 -13 65 -151 146 -14 -28 0 -8 -16 -18 -26 -40 -60 -86 -98)
>> --> norm is 73012
> 
> Superseeker tells me that the sequence above has LDOGF:
> 
>  - (-13/3+52/3*x-8*x^2-2/3*x^3-3*x^4)/(x^5-1/3*x^4+2*x^3-14/3*x^2+7/3*x-1/3)
> 
> A036217 is:         Expansion of 1/(1-3*x)^5
> 
> Now, I open Pari-GP and type:
> 
>  (exp(-log(x^3+x^2+3*x-1)/2+5*log(3*x-1)-log(x-1)/2))/ (1-3*x)^5
> 
> and obviously this is a (new?) generating function for A108626
> 
> Best regards,
> 
> -- 
> Thomas Baruchel


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