On the bivariate Padovan polynomials matrix
Dişkaya, Orhan | Menken, Hamza
In this paper, we intruduce the bivariate Padovan sequence we examine its various identities. We define the bivariate Padovan polynomials matrix. Then, we find the Binet formula, generating function and exponential generating function of the bivariate Padovan polynomials matrix. Also, we obtain a sum formula and its series representation.
On the pulsating Padovan sequence
Dişkaya, Orhan | Menken, Hamza
A novel kind of Padovan sequence is introduced, and precise formulas for the form of its members are given and proven. Furthermore, the pulsating Padovan sequence in its most general form is introduced and the obtained identity is proved.
t-Cobalancing Numbers and t-Cobalancers
Erdem, Alper
In this work, we determined the general terms of all t-cobalancers, t-cobalancing numbers and Lucas t-cobalancing numbers by solving the Pell equation 2x^2-y^2=2t^2-1 for some integer t \geq 1.