Closed form evaluation of restricted sums containing squares of Fibonomial coefficients

Abstract

We give a systematic approach to compute certain sums of squares Fibonomial coefficients with powers of generalized Fibonacci and Lucas numbers as coefficients; the range of the summation is not the natural one but about half of it. The technique is to rewrite everything in terms of a variable q, and then to use generating functions and Rothe's identity from classical q-calculus.