Last Update: Jan. 28, 2018.
No deadline. Contact Neil Sloane if interested. However, if you are an OEIS user, you can submit the sequences to the OEIS yourself. You need to register first: see here.
There are several stages (and even the first, very easy, stage would help the OEIS)
The object is to find the coordination sequence (CS) with respect
to some point P in some 2D or 3D net.
For background information see the article
Chaim Goodman-Strauss and N. J. A. Sloane, The Coloring Book Approach to Finding Coordination Sequences,
which should be available by the end of January 2018 from the OEIS server — see entry
A072154. It should also be available from the arXiv soon after that.
Get first 10 terms of the CSs with respect to the different classes of points in some 2D or 3D net from the RCSR database, and add them to the OEIS if not there already
The RCSR database is RCSR.net. It lists a couple of hundred 2D nets, and 2700 3D nets, Very few of their CSs are in the OEIS so far, so there is plenty for everyone to do!
Once you have the first 10 terms, then either:
look up these sequences in the OEIS and if they are there, add a comment saying
[Appears to be] or [This is also] the coordination sequence with respect to a [trivalent, tetravalent, or ...] point in the [name] 2D or 3D net.
And if the sequence is missing, submit it as a new sequence.
But the RCSR will only show you 10 terms for each type of point. This is often not enough terms to let you guess a formula, or to distinguish it from other sequences in the OEIS.
However, even 10 terms is often enough for a new sequence in the OEIS, if
it is missing, and adding it will help the OEIS.
If you go to the 3D nets section, the third one is the abf net (rcsr.net/nets/abf)
There is a table with three CSs:
vertex cs1 cs2 cs3 cs4 cs5 cs6 cs7 cs8 cs9 cs10 cum10 vertex symbol
V1 4 4 12 24 36 40 84 82 100 148 535 3.3.11(2).11(2).11(2).11(2)
V2 4 8 12 20 48 44 60 98 120 116 531 11(2).11(2).11(2).11(2).11(2).11(2)
V3 3 6 11 21 36 51 65 91 106 142 533 3.11(2).11(4)
Here you can see that there are three kinds of vertex (or point), two are 4-valent (tetravalent) and one is 3-valent (trivalent).
Note that the 0th term a(0)=1 is missing, so you need to add that yourself. Only 10 terms are given, and the rest of the row can be ignored.
So after cleaning up the table, it looks like this:
1,4,4,12,24,36,40,84,82,100,148
1,4,8,12,20,48,44,60,98,120,116
1,3,6,11,21,36,51,65,91,106,142
and I created three OEIS sequences for them: see A298796, A298797, A298798.
You could do the same for any of the 3000 nets in the RCSR database!
OR, to get more terms, we go to the next stage. This is when it starts to get more interesting.
This requires a Windows machine.
Install the ToposPro program from the website topospro.com.
Follow the instructions, and compute about 60 terms of the CSs
you studied in the previous section.
Apparently you can feed ToposPro the definition of the net from the RCSR database.
I've never done this myself, since I don't
have a Windows machine. But I have a MacBook Pro, and there is a Windows machine in the office that share with a dozen other people, so if someone can help me set up ToposPro that would be very nice!
Once you have a decent number of terms, you can add the sequence with confidence to the OEIS.
Or extend the sequence if the OEIS has only 10 terms!
And then:
Study the sequence, and look for a recurrence.
Try to prove it is correct, possibly by using the Coloring Book method described in my paper with Chaim Goodman-Strauss, or by studying the structure of the net.
or by using the gfun program of Salvy and Zimmermann to find a generating function or a recurrence or both. But remember that gfun not give a proof. (You have to say "It appears that the sequence has g.f. ...".)
Postscript I have copies of articles about RCSR and ToposPro, many other articles about CSs, also a preliminary version of the paper with C.G.-S.. Contact me (njasloane at gmail dot com) if interested.