FORMULAS FOR WEIGHTED BINOMIAL SUMS USING THE POWERS OF TERMS OF BINARY RECURRENCES.

In this paper, we give general formulas for some weighted binomial sums, using the powers of terms of certain binary recurrences. As an applications of our results, we show that the weighted binomial sums of the generalized Fibonacci and Lucas numbers can be expressed via the second kinds of Chebyshev polynomials and Stirling numbers. [ABSTRACT FROM AUTHOR]