ON THE REPRESENTATION OF FIBONACCI AND LUCAS NUMBERS IN AN INTEGER BASES

In [10], the circulant matrices involving Fibonacci and Lucas numbers were studied and lower and upper bounds for the spectral norms of these matrices were also given.. In [4],

In [13], Ray introduced Q-balancing matrix and using matrix algebra he obtained several interesting results on sequence of balancing numbers and its related numbers sequences..

The next two properties indicate that, for the fixed points, the study of the Look and Say derivatives can be reduced to the case of words over a three-letter alphabet: indeed

From our point of view it is important that Fibonacci cubes also play a role in mathematical chemistry: Fibonacci cubes are precisely the resonance graphs of fibonacenes which in

Lucas cubes, introduced in [MCS01], have attracted the attention as well due to the fact that these cubes are closely related to the Fibonacci cubes.. They have also been widely

Nice result have been obtained on cube graph of median graphs, and it is thus of interest, from the graph theory point of view, to characterize maximal hypercubes in families of

Key words: hypercubes; cube polynomials; Fibonacci cubes; Lucas cubes; gener- ating functions; zeros of polynomials, unimodal sequences.. AMS subject classifications: 05C31,

The Fibonacci cube of dimension n, denoted as Γ n , is the subgraph of the hypercube induced by vertices with no consecutive 1’s.. Using an interpretation of the irregularity in