Is it possible to determine the number of non-negative integer solutions to $2x + y = N$ where $N$ is a non-negative integer? I was solving a problem when a particular equation of this kind came up and the book simply counted every case (which was rather tedious, given the large amount of cases). Later, I noticed a different problem which appeared to require the same number of solutions of $2x + y = N$ but it was not possible to count the cases because $N$ was not given.
I found another solution and it turned out not be necessary to solve for the number of solutions of the equation, however I'm still wondering if it is possible to find this number in terms of factorials and whatnot. I was not able to do it with the bars/stars method or whatever it's called. So, is it possible?