On-line and Non-line Weighted Generalized Fibonomial Sums

In this paper we consider some new weighted and alternating weighted generalized Fibonomial sums and the corresponding forms. A generalized form of weight sequences which contains squares in subscripts is discussed for the first time in the literature. The main key to get success in sums is an ability to change one sum into another that is simpler in some way. Thus, in order to prove these sums by doing some manipulations and tricks, our approach is to use classical analysis, in particular a formula of Rothe, a version of Cauchy binomial theorem and Gauss identity.