k-POLYCUBES(n) = n*k-POLYOMINOES(n) ?

[magictour at free.fr]

pauldhanna wrote:

 >A048665(n) = n*A093877(n)
 >
 >URL:       http://www.research.att.com/projects/OEIS?Anum=A048665
 >Sequence:  1,8,84,936,10810,127632,1531180,18589840,227826873
 >Name:      Number of rooted 4-dimensional "polycubes" with n cells, with
 >no
 >              symmetries removed.

"rooted" just means, that one cell is specified as root. Divide by n
to get all fixed (don't rotate !) polytesseracts.


 >URL:       http://www.research.att.com/projects/OEIS?Anum=A093877
 >Sequence:  1,4,28,234,2162,21272,218740,2323730,25314097,281299736,
 >           3176220308
 >Name:      Number of fixed n-celled polyzebras (or zebra-move-connected
 >              polyominoes).


A zebra is a (2,3)leaper, which moves 2 squares in any of the 4 directions
parallel to an axes in 2dim and then (same move) 3 squares ortogonal to that.
I assume that we will get the same counts for (m,n)-leapers with m,n>1 coprime.

Or we get the same counts only for small n ??

I won't expect that polytesseracts and polyzebras counts would
coincide for all n just because 4d has more symmetries than 2d.
But this is just a feeling. Somebody feels differently ?
What's the smallest n, where we could expect different counts ?


-Guenter. sterten(at)aol.com