In a recent paper [1] , J. L. Brown, Jr., and R. L, Duncan showed that the sequence *{ QnFn I is uniformly distributed modulo 1 (u.d. mod 1), where c/7 denotes the natural logarithm and Fn is the/? Fibonacci number. In this paper we show that some modifications of these ideas have some interesting consequences concerning the distribution of the first digits of the Fibonacci numbers. This also a...

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...

Protein-fragment seqlets typically feature about 10 amino acid residue positions that are fixed to within conservative substitutions but usually separated by a number of prescribed gaps with arbitrary residue content. By quantifying a general amino acid residue sequence in terms of the associated codon number sequence, we have found a precise modular Fibonacci sequence in a continuous gap-free ...

The generalized Fibonacci cube Qd(f) is the subgraph of the d-cube Qd induced on the set of all strings of length d that do not contain f as a substring. It is proved that if Qd(f) ∼= Qd(f ′) then |f | = |f ′|. The key tool to prove this result is a result of Guibas and Odlyzko about the autocorrelation polynomial associated to a binary string. An example of a family of such strings f , f ′, wh...

We look at binary strings of length n which contain no odd run of zeros and express the total number of such strings, the number of zeros, the number of ones, the total number of runs, and the number of levels, rises and drops as functions of the Fibonacci and Lucas numbers and also give their generating functions. Furthermore, we look at the decimal value of the sum of all binary strings of le...

The characterization of Fibonacci Cobweb poset P as DAG and oDAG is given. The dim 2 poset such that its Hasse diagram coincide with digraf of P is constructed. 1 Fibonacci cobweb poset The Fibonacci cobweb poset P has been invented by A.K.Kwaśniewski in [1, 2, 3] for the purpose of finding combinatorial interpretation of fibonomial coefficients and eventually their reccurence relation. In [1] ...