distinct lattice lines in n dimensions -- interesting enough to submit?

[Joshua Zucker]

I've been working on a sequence or table,
determining the number of distinct lines through
the origin and at least one other lattice point of
the n-dimensional cube of side length k (all coordinates
nonnegative).

For instance,
http://www.research.att.com/projects/OEIS?Anum=A049691
already has the sequence for n = 2.

But I see that there's no real formula there, though it's
not too hard to generate terms in any case.

And I see that
http://www.research.att.com/projects/OEIS?Anum=A049687
already exists, giving the table for rectangles (j,k),
but still in only two dimensions.

I've worked out formulas (messy ones, but they seem to work)
for k = 1 through 7, I think.  For instance, for k = 7
I have 8^n - 4^n - 3^n - 2^n + 2,
which for n = 0 gives 0 as it should,
for n = 1 gives 1 as it should,
and for n = 2 gives 37 which matches A049691,
so I'm pretty confident in my results so far.

So ... should I submit the analogue of A049691
for any other values of n besides n = 2?  Unfortunately
so far I only have the first few terms, though I'm confident
that I can crank out a few more if I need to.

Should I submit the "perpendicular" sequence, as n varies
for fixed k, for any small values of k?

Should I submit the "diagonal" sequence, of n-dimensional
cube of side length n?

Should I submit what I know of the whole square array (n,k)?

In each of the above cases, if you think the sequence
is worth submitting, how many terms should I crank out?

I am sure I want to submit at least one of these sequences ...
the square array, I suppose ... but is superseeker smart enough
to find the rest if I submit only that one?  And if not, I have
no idea if any of the others are interesting enough to be
worth submitting on their own.

Thanks,
--Joshua Zucker
Castilleja School
Palo Alto, CA
http://www.castilleja.org