q-cube enumerator polynomial of Fibonacci cubes

We consider a q-analogue of the cube polynomial of Fibonacci cubes. These bivariate polynomials satisfy a recurrence relation similar to the standard one. They refine the count of the number of hypercubes of a given dimension in Fibonacci cubes by keeping track of the distances of the hypercubes to the all 0 vertex. For q = 1, they specialize to the standard cube polynomials.