The relationship between each term cannot be bijective, however it has a bounded range of finite whole numbers.
Create a rule such that f(x1,y2)=x2 and f(x2,y3) = x3. The rule must be such that after the sequence has been created, if you are given x3,y3,x2 and y1, then x1 and y2 can be determined i.e y2 = g(x2,x3)
I will use the notation x_n for x sub n.
Let's define y1 to be any positive integer, y_(n+1)=y_n + 1 (for instance y_n is 2,3,4,5,...) and x1=1, then define:
x_n=x_(n-1)+100 modulo y_n (so f(x,y)=x+100 mod y). (Just in case you do not know, x modulo y, or x mod y, means the reminder ...
This shows how to create a rule for a sequence that meets specified characteristics.