Yes, the Binet formula is a closed-form. It arises because of a 2nd order linear recursion , which is not the same as the generating function. Also he confuses

Yes, the Binet formula is a closed-form. It arises because of a 2nd order linear recursion , which is not the same as the generating function. Also he confuses the characteristic equation for the generating function. I would recommend a discreate math textbook if you want to learn this.