[seqfan] Sequence A005646, Wexler's Classifications of N Elements

[Robert Munafo]

I have begun a webpage for this sequence, here:

   http://mrob.com/pub/math/seq-a005646.html

The web page has several illustrations, and I believe the explanation is
fairly coherent. I welcome any comments or feedback! (I too found the
one-liner definition to be a bit too cryptic :-)

I want to point out that these results, in particular the values 1015 and
11847, was done with the help (and on the original initiative) of Andrew
Weimholt. He computed them first and I later verified.

However, each of us devised our own algorithms with minimum of communication
on methods, because of the need to verify the accuracy of the results. I
wanted to stay in the dark until I caught up with Andrew. The web page
describes my approach.

On Mon, Dec 28, 2009 at 09:52, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> Any chance you can add an illustration of this sequence?  It's a
> little hard to visualize from its one-line description.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Mon, Dec 28, 2009 at 3:09 AM, Robert Munafo <mrob27 at gmail.com> wrote:
> > I have worked with Andrew Weimholt to confirm his work on the
> > extension of A005646. This is one of the sequences from the 2nd book
> > (Encyclopedia of Integer Sequences), and had not been extended since
> > the late 1970's. The sequence starts 1,1,1,3,6,26,122, to which Andrew
> > added 1015, and I can now confirm that result.
> >
> > The problem represented by this sequence grows very quickly. For N=8
> > one is checking all 7x8 matrices with values of 0 or 1 (in theory,
> > that is 2^56 or 7.2e16 combinations, although some optimizations can
> > be applied reducing this to about 1.2e13). With 16 threads my
> > workstation needs 35 minutes to calculate this answer, but Andrew's
> > implementation is faster.
> > [...]
>

-- 
 Robert Munafo  --  mrob.com