The p-ary function f(x) mapping GF(p) to GF(p) and given by f(x) = Tr4k ( ax + bx ) with a, b ∈ GF(p) and d = p + p − p + 1 is studied with the respect to its exponential sum. In the case when either a (p+1) 6= b +1 or a = b with b 6= 0, this sum is shown to be three-valued and the values are determined. For the remaining cases, the value of the exponential sum is expressed using Jacobsthal sum...

Ladder networks have been studied extensively using Fibonacci numbers, Chebyshev polynomials, Morgan-Voyce polynomials, Jacobsthal polynomials, etc. ([10], [11], [2], [14], [9]. [5], [3], and [4]). All these polynomials are, in fact, particular cases of the generalized polynomials defined by U„(x,y) = xU„_l(x,y)+yU„_2(x,y), (»>2) (la) with U0(x,y) = 0, Ul(x,y) = l, (lb) and V„(x, y) = xV^ix, y)...

In this study, we present higher order Jacobsthal numbers. Then define quaternions by using We give the concept of norm and conjugate for these quaternions. express prove some propositions related to Also, find recurrence relation, Binet formula generating function Finally, calculate Cassini, Catalan, Vajda d’Ocagne identities

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...