in this paper‎, ‎we define two $n$-square upper hessenberg matrices one of which corresponds to the adjacency matrix of a directed pseudo graph‎. ‎we investigate relations between permanents and determinants of these upper hessenberg matrices‎, ‎and sum formulas of the well-known pell and jacobsthal sequences‎. ‎finally‎, ‎we present two maple 13 procedures in order to calculate permanents of t...

In this study, we denote $(t'_{n}(x))_{n\in \mathbb{N}}$ the generalized Tribonacci polynomials, which are defined by $t'_{n}(x)=x^{2}t'_{n-1}(x)+xt'_{n-2}(x)+t'_{n-3}(x), n \geqslant 4,$ with $t_{1}(x)=a, t_{2}(x)=b, t_{3}(x)=cx^{2}$ and drive an explicit formula of in terms their coefficients $T'(n,j)$, Also, establish some properties $(t_{n}(x))_{n\in \mathbb{N}}$. Similarly, study Jacobstha...

This research paper deals with some radius problems, the basic geometricproperties, general coecient and inclusion relations that are established for functionsin a subfamily of analytic functions subordinate to k-Jacobsthal numbers.