In this paper, starting from the shifting property for the ordinary Fibonacci and q-Fibonacci numbers, we obtain some combinatorial identities involving the generalized Fibonacci and q-Fibonacci numbers of the first and second kind, and for the q-Fibonacci polynomials. In particular, we specialize these identities to the Fibonacci polynomials, the Pell polynomials, the Jacobstahl polynomials, the Chebyshev polynomials, the Fermat polynomials and the Morgan-Voyce polynomials.
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