How can you count the initial equity at purchase as part of a dow

[Brian Holt]

How can you count the initial equity at purchase as part of a down payment? Or can we?

Last month this Single Family home was listed for $393,000.  In talking with the seller yesterday they take $349,000.  

For the official offer is it better to write the offer:

1.  Sales price $349,000 and then we (buyer) pay the 20%  OR

2. Sales price $393,000 and they pay $44,000 (11%) at closing and we pay $34,600 to equal the require 20%?

3.  Is it possible to include that price reduction in the original loan amount?  

4.  Any thoughts or other ideas?  We have the 10% but need to sell another property to get the full 20% which will take some time.