In order to avoid confusion let's write the X and Y sequences as...

(1)

(2)

The problem is well attached with the use of the Z-transform. Given a sequence its Z-transform is defined as...

(3)

In term of Z-transform the (1) and (2) are...

(4)

(5)

... and combining (4) and (5) we obtain...

(6)

Now is found performing the inverse Z-transform of (6)...

Kind regards