20 Man, 15 Week Schedule Help

I'm trying to create what should I think be a simple schedule for an upcoming golf league. The schedule should be accomplishing the following:

There are 20 players over a 15 week season.
Each week, you are partnered with someone different.
There should be no duplicate 2 man pairings.

Its' ok if your in the same foursome with someone twice. But you should only ever be partnered with the same person once.

Attached is what I was trying to put together, but I can't quite get the schedule/logic correct.

Any help is appreciated.

Thanks