For distance 0, ...,12 by hand I find number of vertices = 1, 5, 11, 16, 21, 27, 32, 37, 44, 48, 54, 60, 64; and not in OEIS. WFL On 11/17/12, Neil Sloane <njasloane@gmail.com> wrote:
Coordination sequences are of interest to chemists and to combinatorial people. I've written a few papers abut them (see my home page).
One way to define the CS of an infinite graph whose group is transitive on the vertices to let a(n) be the number of vertices whose edge distance from one fixed vertex is n.
Of course there are several ways to define the graph corresponding to a "net" (cf. Wells's book)
There are a lot of coordination sequences in the OEIS - look in the Index under Coordination
Neil
On Fri, Nov 16, 2012 at 7:58 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
On 11/16/12, Allan Wechsler <acwacw@gmail.com> wrote:
There's a pretty Archimedian tiling with vertex figure 3.3.4.3.4 whose vertex coordination sequence has at least one of the following two properties:
The Euclidean plane tiling bearing the same relation to the square lattice as the "snub cube" does to the cuboctahedron in 3-space.
1. It is not in OEIS.
2. I have miscalculated it. (This seems likely, since my "calculation" consisted of scrawling a portion of the tiling and then drawing blobs on vertices while I counted them by hand.)
A segment of the tiling is displayed at http://www.uwgb.edu/dutchs/symmetry/archtil.htm together with a nice comment about its enantiomorph ...
I have the first five elements as 1, 5, 11, 16, 22; OEIS doesn't find anything with those elements. I'll submit this if somebody else can verify my entries.
How exactly do you define this sequence, and why is it interesting?
Fred Lunnon
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