The sum and product of Fibonacci numbers and Lucas numbers, Pell numbers and Pell-Lucas numbers representation by matrix method
نویسندگان
چکیده
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–Words: Fibonacci number; Lucas number; Pell numbers; Pell-Lucas number; matrix.
منابع مشابه
On the sum of Pell and Jacobsthal numbers by matrix method
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...
متن کامل1 INTEGERS 11 A ( 2011 ) Proceedings of Integers Conference 2009 ON THE INTERSECTIONS OF FIBONACCI , PELL , AND LUCAS NUMBERS
We describe how to compute the intersection of two Lucas sequences of the forms {Un(P,±1)}n=0 or {Vn(P,±1)}n=0 with P ∈ Z that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers. We prove that such an intersection is finite except for the case Un(1,−1) and Un(3, 1) and the case of two V -sequences when the product of their discriminants is a perfect square. Moreover, the inter...
متن کاملMathematical Meaning and Importance of the Topological Index Z
The role of the topological index, ZG, proposed by the present author in 1971, in various problems and topics in elementary mathematics is introduced, namely, (i) Pascal’s and asymmetrical Pascal’s triangle, (ii) Fibonacci, Lucas, and Pell numbers, (iii) Pell equation, (iv) Pythagorean, Heronian, and Eisenstein triangles. It is shown that all the algebras in these problems can be easily obtaine...
متن کاملOn the Resolution of the Equations
The purpose of the present paper is to prove that there are finitely many binomial coefficients of the form (f in certain binary recurrences, and give a simple method for the determination of these coefficients. We illustrate the method by the Fibonacci, the Lucas, and the Pell sequences. First, we transform both of the title equations into two elliptic equations and apply a theorem of Mordell ...
متن کاملGeneralized Pell numbers, graph representations and independent sets
In this paper we generalize the Pell numbers and the Pell-Lucas numbers and next we give their graph representations. We shall show that the generalized Pell numbers and the generalized Pell-Lucas numbers are equal to the total number of independent sets in special graphs.
متن کامل