Does anyone know where I can find a crochet pattern for a throw with the Stanford University "S" and/or tree?

I'm not sure where you can find that pattern, but if you don't find it, you might be able to make your own pattern using graphing paper. You can have each block on the paper represent one crochet stitch, or 2, etc. Make your paper's dimensions equal the dimensions that you want the throw to equal. This is what I do whenever I'm designing a throw. :)