Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients

In this paper we evaluate quadratic sums of Gaussian q -binomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of Heine’s transformation, the q -Pfaff–Saalschutz theorem and the q -Kummer sum. Consequently several identities for generalized Fibonomial–Lucanomial coefficients are obtained by specifying the parameter p and the base q .