Separable boolean functions and generalized Fibonacci sequences

On Periodic ∞-generalized Fibonacci Sequences

The notion of an∞-generalized Fibonacci sequence has been introduced in [6], and studied in [1], [7], [9]. This class of sequences defined by linear recurrences of infinite order is an extension of the class of ordinary (weighted) r-generalized Fibonacci sequences (r-GFS, for short) with r finite defined by linear recurrences of r order (for example, see [2], [3], [4], [5], [8] etc.) More preci...

Waiting times and Generalized Fibonacci Sequences

Aitken Sequences and Generalized Fibonacci Numbers

Consider the sequence (t>„) generated by t>„+ ¡ = avn bv,l_l, n 5¡ 2, where v¡ = 1, t>2 = a, with a and b real, of which the Fibonacci sequence is a special case. It is shown that if Aitken acceleration is used on the sequence (x„) defined by a„ = v„+1/v„, the resulting sequence is a subsequence of (jc„). Second, if Newton's method and the secant method are used (with suitable starting values) ...

Octal Generalized Boolean Functions

In this paper we characterize (octal) bent generalized Boolean functions defined on Z2 with values in Z8. Moreover, we propose several constructions of such generalized bent functions for both n even and n odd.

Generalized Boolean Bent Functions

The notions of perfect nonlinearity and bent functions are closely dependent on the action of the group of translations over IF2 . Extending the idea to more generalized groups of involutions without fixed points gives a larger framework to the previous notions. In this paper we largely develop this concept to define G-perfect nonlinearity and G-bent functions, where G is an Abelian group of in...