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    NEW SUMS IDENTITIES IN WEIGHTED CATALAN TRIANGLE WITH THE POWERS OF GENERALIZED FIBONACCI AND LUCAS NUMBERS
    (CHARLES BABBAGE RES CTR, 2014) Kilic, Emrah; Yalciner, Aynur
    In this paper, we consider a generalized Catalan triangle defined by k(m)/n(2n n - k) 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 Sigma(n)(k=0) (2n n + k) k(m)/nX(tk)(r), where X-n 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.
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    On sums of squares of Fibonomial coefficients by q-calculus
    (WORLD SCIENTIFIC PUBL CO PTE LTD, 2016) Kilic, Emrah; Yalciner, Aynur
    We present some new kinds of sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. As proof method, we will follow the method given in [E. Kili, c and H. Prodinger, Closed form evaluation of sums containing squares of Fibonomial coefficients, accepted in Math. Slovaca]. For this, first we translate everything into q-notation, and then to use generating functions and Rothe's identity from classical q-calculus.