q-cube enumerator polynomial of Fibonacci cubes

We also investigate the divisibility properties of the q-analogues and show that the quotient polynomials for the appropriate indices have nonnegative integral polynomials in q as coefficients. These results have many corollaries which include expressions involving the q-analogues of the Fibonacci numbers themselves and their convolutions as they relate to hypercubes in Fibonacci cubes. Many of our developments can be viewed as refinements of enumerative results given by Klavžar and Mollard in (2012).