duplicate hunting

[Artur]

A082745=A064955
Artur



This is one of the seqs where the description is incomplete.
I include a short exchange with Brendan McKay from earlier today:

------------------------

Hi,
thanks for pointing out.  And, no, I do not know
the definition, must be some symmetry thingy.
I'll try to grab the paper when back in Australia.

Thanks for reply!

Cheers,   jj


* Brendan McKay <bdm at cs.anu.edu.au> [May 12. 2008 16:28]:
> Hi Joerg,
>
> Do you know the exact definition?  It can't be non-negative
> integer matrices because it is too obviously wrong.  There
> must be some other missing condition.
>
> For 3*3 matrices of non-neg integers, row&col sums 1, there
> are of course 6.  For sums 2, there are 6 with entries {0,1},
> 6 with entries {2}, and 9 with one 2 and 4 1s; so 21 in total.
> This is A002817.
>
> Cheers, Brendan.

------------------------

* Mitch Harris <maharri at gmail.com> [May 12. 2008 21:20]:
> On Mon, May 12, 2008 at 10:24 AM, Joerg Arndt <arndt at jjj.de> wrote:
> >
> >  * N. J. A. Sloane <njas at research.att.com> [May 10. 2008 22:07]:
> >
> >  > Me:  I agree that many of these are wrong. But are
> >  > you so sure A005045 is wrong?
> >
> >  I cannot test (but hopefully Brendan McKay will be able to help,
> >  if not, I'll do a computation).
> 
> For http://www.research.att.com/~njas/sequences/A005045, "Number of 3
> X 3 matrices with row and column sums n.",
> 
>   - it is very plausible that a 'counting matrices with restriction on
> row/column' has an ogf
>   - the ogf given by Plouffe certainly matches exactly the sequence numbers
>   - but for the life of me I cannot get those numbers by hand from the
> description, nor can I find the article online.
> 
> e.g let n = 1, then I see all row and column sums equal to 1, which is
> obviously a permutation matrix and so there must be 6 matrices then,
> which is different from the 0 that the OEIS seq gives. So I must be
> misunderstanding something.
> 
> Mitch



I think the GF for A067743 is

comment says that seq ==   A000005[n] - A067742[n]
which have GFs:
Sum_{k>0} x^(k^2)*(1+x^k)/(1-x^k)
and

(more forms are given with A000005)

 From these the statement should follow.
However, I am somewhat tired and only got
Hirnverschwurbelung instead of a result.
Anyone care to check?




Yes indeed - I will merge them.
Neil



Mitch,  I found the letter that Elizabeth Morgan
wrote to me on April 6 1978, and i will add
a more precise definition to A005045.

Neil




One of the two PARI maintainers indicates that there are differences
between the Maple V10 number of partitions (combinat[numbpart])
and the current PARI-svn  (the latter based on the Ramanujan-Rademacher
formula see src/modules/part.c). It might be helpful if someone with Mma 
could produce another suite of benchmarks for these n below as some
kind of "third party" counter check:

11269
11566
12376
12430
12700
12754
15013
17589
17797
18181
18421
18453
18549
18597
18885
18949
18997

I do not have access to Mma.

Richard, http://www.strw.leidenuniv.nl/~mathar

kb> I believe Maple is wrong in all cases. Quick check:
kb> 
kb> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
kb> %%
kb> 
kb> ? default(seriesprecision, 12000);
kb> ? polcoeff(1/eta('x),11269)
kb> %2 = 2311391772313039755144117876494556289590601993601099725578515191051551761
kb> 80318215891795874905318274163248033071850
kb> ? numbpart(11269)
kb> %3 = 2311391772313039755144117876494556289590601993601099725578515191051551761
kb> 80318215891795874905318274163248033071850
kb> 
kb> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
kb> %%
kb> 
kb>     |\^/|     Maple 10 (IBM INTEL LINUX)
kb> ._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2005
kb>  \  MAPLE  /  All rights reserved. Maple is a trademark of
kb>  <____ ____>  Waterloo Maple Inc.
kb>       |       Type ? for help.
kb> 
kb> > combinat[numbpart](11269);
kb> 231139177231303975514411787649455628959060199360109972557851519105155176180\
kb>     318215891795874905318274163248033071851
kb> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
kb> %%
kb> 
kb> Cheers,
kb> 
kb>     K.B.