[seqfan] Re: Coord. seqs., the coloring book approach; 2-uniform tilings

[Joerg Arndt]

Sweet!

There are two (trivial) things unclear to me:

Bib entry [16]:
 C. Goodman-Strauss and N. J. A. Sloane, A Tiling Coloring Book, 2018
 (available from the authors).
Is this online somewhere?

The very last page says
"This figure "grid2.png" is available in "png" format from:
 http://arxiv.org/ps/1803.08530v1"
what does "This" refer to?

Best regards,   jj

* Neil Sloane <njasloane at gmail.com> [Mar 28. 2018 11:26]:
> Dear SeqFans, Chaim Goodman-Strauss and I have written up our coloring book
> method for finding coordination seqs, see
> "A Coloring Book Approach to Finding Coordination Sequences",
> https://arxiv.org/abs/1803.08530
> 
> The motivation was to find simple proofs for various conjectured formulas
> in the OEIS (see for example A250120).
> 
> The latter is one of the 11 uniform tilings, see
> 
> List of coordination sequences for uniform planar nets: A008458(the planar
> net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576
> (4.8.8), A008579 (3.6.3.6), A008706(3.3.3.4.4), A072154 (4.6.12), A219529
> (3.3.4.3.4), A250120(3.3.3.3.6), A250122 (3.12.12).
> These now all have g.f.s.
> 
> I've just added all 20 2-uniform tilings to the OEIS, see
> 
> Coordination sequences for the 20 2-uniform tilings in the order in which
> they appear in the Galebach catalog, together with their names in the RCSR
> database (two sequences per tiling): #1 krt A265035, A265036; #2 cph
> A301287, A301289; #3 krm A301291, A301293; #4 krl A301298, A298024; #5 krq
> A301299, A301301; #6 krs A301674, A301676; #7 krr A301670, A301672; #8 krk
> A301291, A301293; #9 krn A301678, A301680; #10 krg A301682, A361684; #11
> bew A008574, A296910; #12 krh A301686, A301688; #13 krf A301690, A301692;
> #14 krd A301694, A219529; #15 krc A301708, A301710; #16 usm A301712,
> A301714; #17 krj A219529, A301697; #18 krc A301716, A301718; #19 krb
> A301720, A301722; #20 kra A301724, A301726.
> 
> Many of these have only the 10 terms that RCSR gives.  If anyone has access
> to ToposPro, that will give 127 terms (the program is free but requires a
> Windows machine).  If we had more terms we could then probably guess a g.f.
> using gfun.
> 
> Even without more terms, our coloring book method should easily produce
> recurrences in most cases, if anyone wants to try it. It is also great fun
> to play with - we were originally going to call the paper "A Child's
> Coloring Book Approach to Finding Coordination Sequences". But children are
> not essential, all you need are colored pencils.
> 
> --
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