n-Uniform Tilings Posted Online

[Brian L. Galebach]

Hello all,

After a programming bug fix and another week or so of computations, I
believe that I have now correctly calculated that a(4)=151 and a(5)=332 in
sequence A068599, which gives the number of n-uniform tilings.  Previously,
I had incorrectly submitted that a(4)=150 and a(5)=328 due to a program
error which incorrectly classified some newly-found tilings as ones that
were already cataloged.  I'm very sorry about that!

While I'm pretty sure that I've got the right answers this time, my
tiling-generation program is quite complicated, and trying to create a proof
that these new values are correct is beyond my capabilities.  Therefore,
what I've done is to post pictures of all the 1- through 5-uniform tilings
that I have generated at http://ProbabilitySports.com/tilings.html.  (Values
for 1- through 3-uniform have already been verified many years ago.)  If
anyone would like to take a look and help me to check whether any of my 4-
or 5-uniform tilings have been duplicated or misclassified, or whether any
possible tilings have been omitted, I would really appreciate it!  Even if
you'd rather not think too hard, I'd encourage you to take a look at them,
since some of these probably never-before-seen tilings are quite pleasant to
behold, and might improve your day just a bit.  :-)

Thanks,
Brian Galebach