In this paper, we introduce a tiling approach to (p,q)-Fibonacci and (p,q)-Lucas numbers that generalize of the well-known Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal ve Jacobsthal-Lucas numbers. We show nth number is interpreted as ways tile 1×n board with cells labeled 1,2,...,n using colored 1×1 squares 1×2 dominoes, where there are p kind colors for q dominoes. Then circular also present...

The main aim of this study is to obtain De Moivre-type identities for Jacobsthal numbers. Also, paper presents a method constructing the second order and third-order numbers Jacobsthal–Lucas Moreover, we give some interesting identities, such as Binet’s formulas specific that derive from identities.

Let p ≡ 1 ( mod 4 ) be a prime. In this paper, with the help of Jacobsthal sums over finite fields, we study some permutation problems involving biquadratic residues modulo .

We study integer sequences associated with the cyclic graph Cr and the complete graph Kr. Fourier techniques are used to characterize the sequences that count walks of length n on both these families of graphs. In the case of the cyclic graph, we show that these sequences are associated with an induced colouring of Pascal’s triangle. This extends previous results concerning the Jacobsthal numbers.

In 1991 Ferri, Faccio and D’Amico introduced and investigated two numerical triangles, called the DFF and DFFz triangles. Later Trzaska also considered the DFF triangle. And in 1994 Jeannin generalized the two triangles. In this paper, we focus our attention on the generalized Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal and Jacobsthal-Lucas polynomials, and several numerical triangles deduce...

Let j(n) denote the smallest positive integer m such that every sequence of m consecutive integers contains an integer prime to n. Let Pn be the product of the first n primes and define h(n) = j(Pn). Presently, h(n) is only known for n ≤ 24. In this paper, we describe an algorithm that enabled the calculation of h(n) for n < 50. 0.