a sequence that needs extending

[Dean Hickerson]

> Regarding sequence A070214 (Maximal number of occupied cells in all
> monotonic matrices of order n), I have confirmed the first five values of
> a(n) and also determined that a(6) = 14 and a(7) = 19.

Thanks for the information.

Does your computation give you a list of some or all of the matrices which
achieve those values?

> A nice feature of an integer programming approach is that upper bounds are
> available throughout the computation, so that we have some measure of the
> quality of the current best known solutions.  For example, I know that
> a(8) <= 30, so Dean's 23-cell solution is at most 7 away from optimal.

Based on your experience with a(6) and a(7), do you expect that the upper
bound will gradually decrease as the program runs, or make a sudden drop
to the correct value when the program finishes?

Dean Hickerson
dean at math.ucdavis.edu