All depends! :)
Here's the run down. Lp is the gene that makes an appy (characteristics only). PATN1 is what makes an Lp horse into a leopard. So the horses are both Lplp PATN1_. They can't be LpLp because that turns a leopard into a few spot. Can't say if they're PATN1PATN1 or PATN1patn1 just by looking at them.
So, if one parent throws Lp and the other doesn't, and at least one throws PATN1, (Lplp PATN1_) you'll get a leopard.
If both give Lp and at least one gives PATN1 (LpLp PATN1_) you'll have a few spot.
If neither give Lp, it doesn't matter about the PATN1, (lplp _ _) you'll have a solid, non-charactieristic foal.
If one or both give Lp but neither give PATN1, (Lp_ patn1patn1) you'll have a characteristic only foal in theory (I say in theory because either parent might have some other PATN gene that could be passed on, such as a small blanket or something.)
So, you never know! The joys of breeding appaloosas.... ;)