I have an equation that looks like: $x_1+x_2+x_3+x_4+x_5+x_6 = n.$ ($n$ is a natural number ).
Let A be the number of solutions under these conditions: $x_1,x_3$ are even & $x_3 \le 20$. $x_6 \gt x_2+x_4$.
Let B be the number of solutions under these conditions: $x_1,x_2,x_3,x_4$ are even. $x_5 \ge 1.$ $x_6 \le 41.$
I need to use generating functions in order to prove that A=B.
however, I am stuck with dealing with the case $x_6 \gt x_2+x_4.$ I thought of defining $a>0$ , so $x_6 = x_2+x_4+a$. but I dont know how to continue on from there.