[seqfan] Re: how to scan a 3D array

Neil Sloane njasloane at gmail.com
Mon Dec 7 16:49:03 CET 2015


We don't have a standard way to linearize 3-D arrays.

The few examples that are in the OEIS were scanned in
what seemed to be the best way for the particular array in question.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Mon, Dec 7, 2015 at 10:13 AM, Chris Starling <chaosorder4 at gmail.com>
wrote:

> Hello, sequence people...
>
> Longtime lurker here.
>
> I have quite a few 3D arrays of integers, based on quantities for
> trivariate figurate forms.  With these, typically, there are three sets of
> edges on a figurate form, each of which have a unit count.  When those
> three counts are plugged into a formula, a total units quantity for that
> figurate form is found, and that can go into the sequence.
>
> But the question is, where in the sequence?
>
> I have seen sequences that are  2D arrays, and in the description is,
> "triangle read by rows", which is understandable enough.  But there are at
> least two ways of doing that.  For the same 2D array, one could repeatedly
> scan from UR to LL diagonally, or from LL to UR.  For a third possibility,
> one could alternate, so that there is always array adjacency preserved
> between any two neighbors in the sequence.  And it gets expectably more
> complex with 3D.  There are at least six ways to do carriage-return linear
> scans, before considering adjacency and spirals.
>
> So what I'm wondering is, is there some convention, based on the
> distinctions between variables, or should I just pick one way, and label
> how I scanned it?
>
> An example array starts as follows:
>
>     1
>
>     6    4
>   13
>
>   19  16  10
>   38  28
>   55
>
>   44  40  31  20
>   79  68  50
> 116  92
> 147
>
> The UL corner of each triangle is an octahedron, the UR is a tetrahedron,
> and the bottom corner is a cuboctahedron.  These are quantities of spheres
> packed in FCC.  The rest are in the field of varying truncation between
> those, that grows with each layer.
>
> Just like with 2D arrays, there are multiple smaller order sequences
> automatically included within it.
>
> Any help or guidance will be much appreciated.
> Sincerely, Chris.
>
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