On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients

ON THE GENERALIZED ORDER-k FIBONACCI AND LUCAS NUMBERS

In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.

Sums of products of generalized Fibonacci and Lucas numbers

In this paper, we establish several formulae for sums and alternating sums of products of generalized Fibonacci and Lucas numbers. In particular, we recover and extend all results of Z. Čerin [2, 2005] and Z. Čerin and G. M. Gianella [3, 2006], more easily.

Some New Finite Sums Involving Generalized Fibonacci And Lucas Numbers

Negativity Subscripted Fibonacci And Lucas Numbers And Their Complex Factorizations

In this paper, we …nd families of (0; 1; 1) tridiagonal matrices whose determinants and permanents equal to the negatively subscripted Fibonacci and Lucas numbers. Also we give complex factorizations of these numbers by the …rst and second kinds of Chebyshev polynomials. 1. Introduction The well-known Fibonacci sequence, fFng ; is de…ned by the recurrence relation, for n 2 Fn+1 = Fn + Fn 1 (1.1...

Trigonometric Expressions for Fibonacci and Lucas Numbers

The amount of literature bears witness to the ubiquity of the Fibonacci numbers and the Lucas numbers. Not only these numbers are popular in expository literature because of their beautiful properties, but also the fact that they ‘occur in nature’ adds to their fascination. Our purpose is to use a certain polynomial identity to express these numbers in terms of trigonometric functions. It is in...