In this paper, we consider the relationships between the second order linear recurrences and the permanents and determinants of tridiagonal matrices. 1. Introduction The well-known Fibonacci, Lucas and Pell numbers can be generalized as follows: Let A and B be nonzero, relatively prime integers such that D = A 4B 6= 0: De…ne sequences fung and fvng by, for all n 2 (see [10]), un = Aun 1 Bun 2 (...

In our previous report [5], we developed some methods ie the study of the line-sequential properties of the polynomial sequences treated in Shannon and Horadam [9]. In this report, we work out the properties for the general case and apply them to the Pell polynomial line-sequence as an example. Some known results are included for completeness, but only new aspects will be presented in some deta...

We consider sequences of the type An = 6An−1 − An−2, A0 = r, A1 = s (r and s integers) and show that all sequences that solve particular cases of the Pell generalized equation are expressible as a constant times one of four particular sequences of the same type. Let α = 3 + 2 √ 2, β = 3 − 2 √ 2 be the roots of the polynomial x − 6x+ 1. Note that α+β = 6, αβ = 1, α−β = 4 √ 2. Also let γ = 1+ √ 2...