Sums of powers of Fibonacci and Lucas polynomials in terms of Fibopolynomials

We consider sums of powers of Fibonacci and Lucas polynomials of the form Sigma(q)(n= 0) F-tsn(k) (x) and Sigma(q)(n=0) L-tsn(k) (x), where s, t, k are given natural numbers, together with the corresponding alternating sums Sigma(q)(n=0) (-1)(n) F-tsn(k) (x) and Sigma(q)(n=0) (-1)(n) L-tsn(k) (x). We give conditions on s, t, k for express these sums as some proposed linear combinations of the s-Fibopolynomials ((tk) (q+m))(Fs(x)), m = 1, 2,..., tk.