On the properties of k-balancing numbers

Prasanta Kumar Ray
2016 Ain Shams Engineering Journal  
In this study, a generalization of the sequence of balancing numbers called as k-balancing numbers is considered and some of their properties are established. Further, the balancing polynomials that are the natural extension of k-balancing numbers are presented and observe that many of their properties admit straightforward proofs. The derivatives of these polynomials in the form of convolution are also discussed. Ó 2016 Faculty of Engineering, Ain Shams University. Production and hosting by
more » ... evier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
doi:10.1016/j.asej.2016.01.014 fatcat:tfl32gsljvbg3kd55jyhtgvz7q