A k-nacci sequence in a finite group is a sequence of group elements x0, x1, x2, . . . , xn, . . . for which, given an initial seed set x0, x1, x2, . . . , xj−1 , each element is defined by xn x0x1 . . . xn−1, for j ≤ n < k, and xn xn−kxn−k 1 . . . xn−1, for n ≥ k. We also require that the initial elements of the sequence, x0, x1, x2, . . . , xj−1, generate the group, thus forcing the k-nacci s...

a k-nacci sequence in a finite group is a sequence of group elements x0 , x1, x2 ,, xn , forwhich, given an initial (seed) set 0 1 2 1 , , , ,j x x x x  , each element is defined by0 1 11 1for ,for .nnn k n k nxx x j n kxx x x n k        in this paper, we examine the periods of the k-nacci sequences in miller’s generalization of the polyhedralgroups 2,2 2;q , n,2 2;q , 2, n 2;...

How would Fibonaccis age-old sequence be redefined if, instead of bearing one pair of baby rabbits per month, the mature rabbits bear two pairs of baby rabbits per month? The answer is an intriguing sequence that has led to the development of what are herein defined as "multi-nacci sequences of the order q <," where q is the number of rabbit pairs per litter. Table 1 illustrates the sequence wi...

Initial numbers for Lucas? type series have so far been established only Fibonacci (2,1) and Tribonacci (3,1,3) sequences. Characteristics of stated is their asymptotic relation with the exponent constant. By using a simple procedure based on relations exponents sequences constant application Nearest Integer Function - NIF, general rule initial Generalized sequence has established, first time. ...

We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the β-numeration. A matrix decomposition of these measures is obtained in the case when β is a PV number. We also determine their Gibbs properties for β being a multi-nacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.

Mobile devices have become the main interaction mean between users and the surrounding environment. An indirect measure of this trend is the increasing amount of security threats against mobile devices, which in turn created a demand for protection tools. Protection tools, unfortunately, add an additional burden for the smartphone’s battery power, which is a precious resource. This observation ...

We define the convolved hðxÞ-Fibonacci polynomials as an extension of the classical con-volved Fibonacci numbers. Then we give some combinatorial formulas involving the hðxÞ-Fibonacci and hðxÞ-Lucas polynomials. Moreover we obtain the convolved hðxÞ-Fibo-nacci polynomials from a family of Hessenberg matrices. Fibonacci numbers and their generalizations have many interesting properties and appli...