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

[Paul D. Hanna]

Seqfans, 
        Is there a known direct correlation between 
k-dimensional polyominoes and polycubes?  
For it appears that 
        k-POLYCUBES(n) = n*k-POLYOMINOES(n) 
This seems intuitive enough, yet it appears that the authors 
of the sequences (see below) are unaware of this (if true). 
  
Can someone supply references or theory or comments that 
would support or qualify or counter this conjectured relation? 
 
If true, then some of these sequences could be readily extended.
 
Thanks,
         Paul
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POLYCUBES: 
Number of rooted m-dimensional polycubes with n cells, 
with no symmetries removed:
 
http://www.research.att.com/projects/OEIS?Anum=A048664
http://www.research.att.com/projects/OEIS?Anum=A048663
http://www.research.att.com/projects/OEIS?Anum=A048665
http://www.research.att.com/projects/OEIS?Anum=A048666
http://www.research.att.com/projects/OEIS?Anum=A048667
http://www.research.att.com/projects/OEIS?Anum=A048668
http://www.research.att.com/projects/OEIS?Anum=A094101
  
 
POLYOMINOES: 
Number of fixed m-dimensional polyominoes with n cells:
 
http://www.research.att.com/projects/OEIS?Anum=A001168
http://www.research.att.com/projects/OEIS?Anum=A001931
http://www.research.att.com/projects/OEIS?Anum=A093877
 
 
CONJECTURES (examples copied at bottom) - true for all n>0?
 
A048664(n) = n*A001168(n)
A048663(n) = n*A001931(n)
A048665(n) = n*A093877(n)
 
 
EXTENSION. 
What then can be said about the combinatorial interpretation 
of these sequences: 
  
A048666(n)/n = ?
A048667(n)/n = ?
A048668(n)/n = ?
A094101(n)/n = ?
 
for n>0.
 
 
EXAMPLES (not all terms are shown here).
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A048664(n) = n*A001168(n)

URL:       http://www.research.att.com/projects/OEIS?Anum=A048664
Sequence:  1,4,18,76,315,1296,5320,21800,89190,364460,1487948,6070332,
Name:      Number of rooted 2-dimensional polyominoes with n square
cells, with
              no symmetries removed.
 
URL:       http://www.research.att.com/projects/OEIS?Anum=A001168
Sequence:  1,2,6,19,63,216,760,2725,9910,36446,135268,505861,1903890,
Name:      Number of fixed polyominoes with n cells.
 
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A048663(n) = n*A001931(n)
 
URL:       http://www.research.att.com/projects/OEIS?Anum=A048663
Sequence:  1,6,45,344,2670,20886,164514,1303304,10375830,82947380,
Name:      Number of rooted polycubes with n cells, with no symmetries
removed.
 
URL:       http://www.research.att.com/projects/OEIS?Anum=A001931
Sequence:  1,3,15,86,534,3481,23502,162913,1152870,8294738,60494549,
Name:      Number of fixed 3-dimensional polyominoes with n cells;
lattice
              animals in the simple cubic lattice (6 nearest neighbors),
              face-connected cubes.
 
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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.
 
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).
 
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END.