[seqfan] Re: My tool for exploring sequences

[Neil Sloane]

Thomas, That is interesting.  Can you add the appropriate comments
to those sequences? The relation between A000166 and A135799, for example,
is certainly worth putting on record.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Fri, Jan 8, 2016 at 8:54 AM, Thomas Baruchel <baruchel at gmx.com> wrote:

> On Mon, 21 Dec 2015, Alexander Povolotsky wrote:
>
>> Sure - I appreciate your method and your efforts!
>>
>
> Hi, after these holydays, I would like to wish you a happy new year to all
> of you.
> I want also to take some time to illustrate how to use my tool.
>
> I spent ~5-10 minutes browsing the OEIS database for choosing a sequence.
> I finally took A000166 :
>
>     Subfactorial or rencontres numbers, or derangements: number of
>     permutations of n elements with no fixed points.
>     (Formerly M1937 N0766)
>     1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570,
>     176214841, 2290792932, ...
>
> There are some more terms, but I exactly copied the first ones which I
> used with
> my tool; I typed:
>
>   java -jar oeis-deconvolution2-1.0.0-standalone.jar \
>   -d ../../oeis-deconvolution/stripped.gz \
>   "1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, \
>   14684570, 176214841, 2290792932"
>
> Here is the output of my program; I give some comments below:
>
>     OEIS/deconvolution by Th. Baruchel
>       initial norm = 5279001364251477795
>     Deconvolution with A000166:
>       is (1 0 0 0 0 0 0 0 0 0 0 0 0 0)
>       --> norm is 1
>     Deconvolution with A002741:
>       is (1 1 0 0 0 0 0 0 0 0 0 0 0 0)
>       --> norm is 2
>     Deconvolution with A135799:
>       is (1 0 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048)
>       --> norm is 5592406
>     Deconvolution with A173184:
>       is (1 -1 0 0 0 0 0 0 0 0 0 0 0 0)
>       --> norm is 2
>     Deconvolution with A257953:
>       is (1 0 0 0 0 0 0 0 0 0 0 0 0 0)
>       --> norm is 1
>     Deconvolution with A260091:
>       is (1 0 0 0 0 0 0 0 0 0 0 0 0 0)
>       --> norm is 1
>     Deconvolution with A260111:
>       is (1 0 0 0 0 0 0 0 0 0 0 0 0 0)
>       --> norm is 1
>     Deconvolution with A260115:
>       is (1 0 0 0 0 0 0 0 0 0 0 0 0 0)
>       --> norm is 1
>     Deconvolution with A260216:
>       is (1 0 0 0 0 0 0 0 0 0 0 0 0 0)
>       --> norm is 1
>
> First of all, this is the output with the default settings, and it looks
> not too
> bad at all; with other sequences, it may be useful to change the -t
> setting.
>
>   a) The sequence is detected in the database: A000166 (first result)
>   b) A connected sequence A002741 is detected (but A000166 already tells
> about
>      this connection).
>   c) The program also detects something marvelous with A135799, but A000166
>      doesn't seem to be aware of that; have a closer look...
>      The page for A135799 doesn't tell either about A000166, but A135799
> depends
>      itself of A134832 which doesn't tell about A000166 either...
>      Let's go back to A135799 which tells about A000757 and finally we find
>      a relation between A000757 and A000166.
>      Maybe something more direct could be found?
>      My tools computes as a resulting sequence:
>        (1 0 1 -2 4 -8 16 -32 64 -128 256 -512 1024 -2048)
>        which is obviously related to generating sequence 1/(2*x+1)
>        The exact G.f. actually is: 1+x^2/(2*x+1) in case it would be
> important.
>      Thus, if I am not wrong, any G.f. for A000166 divided by 1+x^2/(2*x+1)
>      should be a generating function for A135799. There are many
> complicated
>      G.f. for the first one and almost nothing for the second one, maybe
>      something interesting for A135799 would be worth being kept?
>   d) A connected sequence A173184 is detected; nothing surprising since
> A173184
>      is defined with A000166; maybe it would be worth adding a link to
> A173184
>      from A000166?
>   e) A257953 is a sublist of A000166;
>   etc.
>
> I may post about another sequence in some time if I find another example,
> but
> I hope it can help to understand the idea...
>
>
> Regards,
>
> --
> Thomas Baruchel
>
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