We consider a parameterized family of Thue equations of degree 16. By a generalization of Tzanakis’ method we reduce this family to a system of Pell equations and linear relations.

In order to study the density of the set of positive integers d for which the negative Pell equation x2 − dy2 = −1 is solvable in integers, we compute the norm of the fundamental unit in certain well-chosen families of real quadratic orders. A fast algorithm that computes 2-class groups rather than units is used. It is random polynomial-time in log d as the factorization of d is a natural part ...

In [W2] West conjectured that there are 2(3n)!/((n+1)!(2n+1)!) two-stack sortable permutations on n letters. This conjecture was proved analytically by Zeilberger in [Z]. Later, Dulucq, Gire, and Guibert [DGG] gave a combinatorial proof of this conjecture. In the present paper we study generating functions for the number of two-stack sortable permutations on n letters avoiding (or containing ex...

In this paper, we examine the tilings of a 2 × n “triangular strip” with triangles. These tilings have connections with Fibonacci numbers, Pell numbers, and other known sequences. We will derive several different recurrences, establish some properties of these numbers, and give a refined count for these tilings (i.e., by the number and type of triangles used) and establish several properties of...

We introduce and study an invertible transformation on integer sequences related to the Catalan numbers. Transformation pairs are identified among classical sequences. A closely related transformation which we call the generalized Ballot transform is also studied, along with associated transformations. Results concerning the Fibonacci, Jacobsthal and Pell numbers are derived. Finally, we derive...

College participation among “non-traditional” students including women with children has increased markedly in the last three decades. This increase is likely to reflect both changes in labor market opportunities and federal financial aid relieving credit constraints and reducing the direct cost of college. For women with children, the need to finance childcare may impede investment in skills t...

The goal of this study is to develop some new connection formulae between two generalized classes Fibonacci and Lucas polynomials. Hypergeometric functions the kind 2F1(z) are included in all coefficients for a specific z. Several famous polynomials, such as Fibonacci, Lucas, Pell, Fermat, Pell–Lucas, Fermat–Lucas deduced special cases derived formulae. Some introduced generalize those existing...