[seqfan] Re: Higher dimensional analogues to plane division by ellipses?

[Neil Sloane]

Jess, look at the cross-references in A014206!
Here are a few of them:
Cf. A014206 <https://oeis.org/A014206> (dim 2),
A046127<https://oeis.org/A046127> (dim
3), A059173 <https://oeis.org/A059173> (dim 4),
A059174<https://oeis.org/A059174> (dim
5). A row of A059250 <https://oeis.org/A059250>.


On Fri, May 31, 2013 at 3:47 PM, Jess Tauber <goldenratio at earthlink.net>wrote:

> OEIS A051890 relates to the maximal number of regions into which
> ellipsoids may divide the plane. A014206 for division of the plane by
> circles.
>
> I've seen BOTH these sequences with regard to the combinatorics of
> nucleons in real nuclei.
>
> All sorts of questions come to mind, but I'll limit myself to these:
>
> Firstly, are there analogous sequences for higher dimensional analogues,
> say, volume elements in a larger volume cut by ellipsoids or spheres, and
> are the formulae regularly relatable to those of the plane?
>
> Secondly, what if we consider other conic sections (and higher analogues),
> either uniformly or in combination?
>
> I tried looking up volume division at the Wolfram site, no luck.
>
> Thanks.
>
> Jess Tauber
> goldenratio at earthlink.net
>
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>



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