New sums identities in weighted catalan triangle with the powers of generalized fibonacci and lucas numbers

In this paper, we consider a generalized Catalan triangle defined by k m/n (2n/n-κ) for positive integer m. Then we compute the weighted half binomial sums with the certain powers of generalized Fibonacci and Lucas numbers of the form Σnk=0(2n/n+κ) km/n Xrtk, where Xn either generalized Fibonacci or Lucas numbers, t and r are integers for 1 < m < 6. After we describe a general methodology to show how to compute the sums for further values of m.