[seqfan] Re: Maximal number of touching points between unit spheres

[Richard J. Mathar]

Related to http://list.seqfan.eu/pipermail/seqfan/2018-February/018394.html

My explicit computation for clusters of spheres centered on the f.c.c.
lattice gives 0,1,3,6,8,12,15,... for A214813: a discrepancy at
a(5). [I checked that my number of configurations equals A038173.]

There is a sentence in Bezdeks "Contact numbers..." Disc. Comput. Geom (2012)
saying "if this were true,... if would follow that C_fcc(5)=9", which
might be the reason why currently a(5)=9. 

So the question is: 
is A214813(5)=9 correct, perhaps referring to unconstrained/disordered sphere
packings, or do we need to change either the definition or the numbers, or is my
analysis just wrong and missing configurations with 5 spheres on the f.c.c.
lattice? Can anyone provide the sphere center coordinates of 5 spheres
in a f.c.c. lattice with 9 contacts, as claimed in A214813?

Richard