×

zbMATH — the first resource for mathematics

Generalized transformations on ratios of Fibonacci and Lucas numbers. (English) Zbl 0860.11006
The authors consider generalized Fibonacci sequences \((u_n)\) and generalized Lucas sequences \((v_n)\), both satisfying the recurrence \(x_{n+1} = px_n- qx_{n-1}\). They study the behaviour of the quotients \(\left( {u_{n+d} \over u_n} \right)\) under transformations of the Newton type \[ N(x)= x-{f(x) \over f'(x)} \quad \text{with} \quad f(x)= x^2-v_dx+ q^d. \] Extensions of the well-known formula \[ N \left({u_{n+d} \over u_n} \right)= {u_{2n +d} \over u_{2n}} \] are shown.
Reviewer: R.F.Tichy (Graz)
MSC:
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
PDF BibTeX XML Cite