Conjugate m-dimensional partitions

[Max]

On 5/13/06, franktaw at netscape.net <franktaw at netscape.net> wrote:

> I have submitted that table as pre-numbered sequence A119269.  It looks
> like you have a few more values; please extend it once it's out there
> (which should be soon).

OK.

> Your three "guessed" values are correct, assuming the accuracy of your
> other numbers.  The final increments in the columns become fixed (as
> you conjecture) once you get to twice the dimension;

Do you have a proof for that?

> in reverse order,
> 1, 2, 6, 19, and (from your numbers) 60.  This could be A052544, but I
> have no particular reason to think it is.

It may be also interesting to consider partial sums of that sequence which is
s(k): 0, 0, 1, 3, 9, 28, 88  (for k=1..7)
so that for any fixed k and large enough m,
T(m,m+k) = a(m+k) - s(k)
where a(n) = T(n-2,n) is the number of infinity-dimensional partitions
of n up to conjugacy.

Max