Negatively Subscripted Fibonacci and Lucas Numbers and Their Complex Factorizations

E. Kilic1, D. Tasci2
1TOBB ECONOMICS AND TECHNOLOGY UNIVERSITY MATHEMATICS DEPARTMENT 06560 ANKARA TURKEY
2Gazi University, DEPARTMENT OF MATHEMATICS, 06500 ANKARA TURKEY

Abstract

In this paper, we find families of \((0, -1, 1)\)-tridiagonal matrices whose determinants and permanents equal the negatively subscripted Fibonacci and Lucas numbers. Also, we give complex factorizations of these numbers by the first and second kinds of Chebyshev polynomials.