  In this paper we find closed form for the generating function of powers of
any non-degenerate second-order recurrence sequence, completing a study begun
by Carlitz and Riordan in 1962. Moreover, we generalize a theorem of Horadam on
partial sums involving such sequences. Also, we find closed forms for weighted
(by binomial coefficients) partial sums of powers of any non-degenerate
second-order recurrence sequences. As corollaries we give some known and
seemingly unknown identities and derive some very interesting congruence
relations involving Fibonacci and Lucas sequences.
