Number of integral solution of $x+2y=n$ using generating function

Question

I want to know, how to calculate the number of integral solutions of $x+2y=n$.

Answer 1

Assuming that you want positive integr solutions of $x+2y=n$ is $y=1, x=n-2$ Check that $x=n-2+2m, y=1-m$ then the condition that $x,y > 0$ implies that $-[(n-2)/2] < m < 1$, [.] denotes the integer part total number os solutions are $n/2-1$ if $n$ is even or $(n-1)/2$.