[seqfan] Re: Breaking news on partition numbers.

[Alexander P-sky]

I by the way ran the below subset of A034891 via the superseeker
Besides recognizing that terms belong to A034891 superseeker's
GUESSGF also came up with ogf guess - is it different sequence ?

Report on [ 1,2,3,4,6,8,11,14,18,23,29,36,45,55,67,81,98,117,140,166,196]:
Many tests are carried out, but only potentially useful information
(if any) is reported here.

SUGGESTION: GUESSGF FOUND ONE OR MORE GENERATING FUNCTIONS
WARNING: THESE MAY BE ONLY APPROXIMATIONS!
Generating function(s) and type(s) are:

                       2   3       4      5       6     7        8    9    10
     -2 - 3 x - 2 x  - x  - 2 x  - 3 x  - 2 x  + x  + 2 x  - x  - x
  [- ----------------------------------------------------------------, ogf]
                         8    9      2       6       5     7
               2 + 2 x  - x + 2 x  - 2 x  - 2 x  + x  - x

On 1/25/11, Alexander P-sky <apovolot at gmail.com> wrote:
> FYI - there is already discussion at mathoverflow which is following
> the trail of this seqfan thread
>
> http://mathoverflow.net/questions/53205/computability-of-oeis-a034891-partitions-of-n-into-prime-parts-1-included
>
> ARP
> --------- Forwarded message ----------
> From: Charles Greathouse <charles.greathouse at case.edu>
> Date: Tue, 25 Jan 2011 13:50:05 -0500
> Subject: [seqfan] Re: Breaking news on partition numbers.
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>
>> I cannot, however, see how much more can be read from this picture
>> and certainly not something worth calling "model" of any sort,
>> though I am happy to be proven wrong here.
>
> Of course this is what I'm looking for: something to prove your (and
> my) intuition wrong.  It's not an isolated event, either: there are a
> great many sequences submitted without any apparent motivating
> factors.  If there is an interesting sequence that is submitted
> without explanation, my concern is that someone might happen upon that
> sequence later (remember, it is by assumption interesting) and *not*
> learn anything about it because the author left off that explanation.
>
> I believe in Neil's old rule of thumb here: a sequence should take at
> least an hour to create, between research, referencing, calculating,
> and writing.*  If you can't be bothered to spend that much time, the
> sequence might not be interesting enough for inclusion (but rather as
> a comment to an existing sequence, perhaps).
>
> * This is not a complaint against those who submit many sequences at a
> time, like R. H. Hardin; presumably a great deal of time is spent
> preparing his sequences which are then submitted in batches.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On 1/25/11,  wrote:
>> * Charles Greathouse <charles.greathouse at case.edu> [Jan 25. 2011 10:03]:
>>> Can you explain why those sequences are interesting?
>>>
>>> http://www.polprimos.com/imagenespub/polpa3dt.jpg
>>> is a fine illustration of A000041, but I don't immediately see the
>>> value of these sequences.
>>>
>>
>> As far as I can see this is an illustration of the fact that
>> the partitions of n can be split into
>> A) partitions of n-1 with the part 1 appended
>> B) partitions without the part 1
>>
>> This shows that the numbers of partitions without part 1
>> are the differences of the numbers of partitions,
>> a nice "proof without words".
>>
>> I cannot, however, see how much more can be read from this picture
>> and certainly not something worth calling "model" of any sort,
>> though I am happy to be proven wrong here.
>>
>> Until this happens I'll remain the usual grumpy German,
>> also known as Sauer Kraut.
>>
>> cheers,   jj
>>
>>> [...]
>