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...

It was proven by Emma Lehmer that for almost all odd primes p, F2p is a Fibonacci pseudoprime. In this paper, we generalize this result to Lucas sequences {Uk}. In particular, we find Lucas sequences {Uk} for which either U2p is a Lucas pseudoprime for almost all odd primes p or Up is a Lucas pseudoprime for almost all odd primes p.

In this paper, we introduce a q-analog of the bi-periodic Lucas sequence, called as the q-bi-periodic Lucas sequence, and give some identities related to the q-bi-periodic Fibonacci and Lucas sequences. Also, we give a matrix representation for the q-bi-periodic Fibonacci sequence which allow us to obtain several properties of this sequence in a simple way. Moreover, by using the explicit formu...

Several of the economically interesting aspects of the Uzawa-Lucas model are not really emphasized in the exposition in B & S, Section 5.2.2, which instead focusses on quite technical aspects such as the transitional dynamics of (a simplified version of) the model. Hence, in this lecture note I shall attempt to give an account of the Uzawa-Lucas model which closer to the presentation in Lucas (...

human capital has always been of high importance in economic growth literature. in this regard, several studies have tried to explain the role of this variable via the use of different models. the present study, in line with the previous ones, going to estimate the share of human capital in iranian economy production from 1974 to 2011 within the framework of ozawa (1965) and lucas’s (1988) endo...

Denote by {Fn} and {Ln} the Fibonacci numbers and Lucas numbers, respectively. Let Fn = Fn × Ln and Ln = Fn + Ln. Denote by {Pn} and {Qn} the Pell numbers and Pell-Lucas numbers, respectively. Let Pn = Pn × Qn and Qn = Pn + Qn. In this paper, we give some determinants and permanent representations of Pn, Qn, Fn and Ln. Also, complex factorization formulas for those numbers are presented. Key–Wo...

Lucas chains are a special type of addition chains satisfying an extra condition: for the representation ak = aj + ai of each element ak in the chain, the difference aj − ai must also be contained in the chain. In analogy to the relation between addition chains and exponentiation, Lucas chains yield computation sequences for Lucas functions, a special kind of linear recurrences. We show that th...