combinatorics of graphs on lattice

Hi,

I stumbled on the following problem:

Given an nxn grid and all possible graphs on it with number of edges E
and where each edge must be either horizontal or vertical, how many of
these graphs have a spanning forest of size F?

I'm not a mathematician and don't realy know where to look for possible
solutions to this problem. If anybody could give some pointers I would
be very happy!

Thanks
Geert-Jan van Opdorp

.

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