In this paper, we define the Fibonacci–Jacobsthal, Padovan–Fibonacci, Pell–Fibonacci, Pell–Jacobsthal, Padovan–Pell and Padovan–Jacobsthal sequences which are directly related with Fibonacci, Jacobsthal, Pell Padovan numbers give their structural properties by matrix methods. Then obtain new relationships between numbers.

We consider a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this family of meta-Fibonacci sequences and two families of related sequences we derive ordinary generating functions and recurrence relations. Included in these fami...

We discuss an equivalence relation on the set of square binary matrices with the same number of 1’s in each row and each column. Each binary matrix is represented using ordered n-tuples of natural numbers. We give a few starting values of integer sequences related to the discussed problem. The obtained sequences are new and they are not described in the On-Line Encyclopedia of Integer Sequences...

We show that the Conway polynomials of Fibonacci links are Fibonacci polynomials modulo 2. We deduce that, when n 6≡ 0 (mod 4) and (n, j) 6= (3, 3), the Fibonacci knot F (n) j is not a Lissajous knot. keywords: Fibonacci polynomials, Fibonacci knots, continued fractions

Abstract We consider an identity relating Fibonacci numbers to Pascal’s triangle discovered by G. E. Andrews. Several authors provided proofs of this identity, all of them rather involved or else relying on sophisticated number theoretical arguments. We not only give a simple and elementary proof, but also show the identity generalizes to arrays other than Pascal’s triangle. As an application w...

We know that the Fibonacci numbers count the tilings of a (1×n)-board by squares and dominoes, or equivalently, the number of tilings of a (2×n)-board by dominoes. We use the tilings of a (2×n)-board by colored unit squares and dominoes to obtain some new combinatorial identities. They are generalization of some known combinatorial identities and in the special case give us the Fibonacci identi...

the objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a fibonacci hypercube structure. most of the popular algorithms for parallel matrix multiplication can not run on fibonacci hypercube structure, therefore giving a method that can be run on all structures especially fibonacci hypercube structure is necessary for parallel matr...

Notation (i) RFN (Random Fibonacci Number: An I -digit (I > 2) Fibonacci number whose subscript has been randomly chosen within the interval [Kx, K2], where Kx > 7 and K2 is much greater than Kv (ii) B(d): the probability that the initial digit of a EFN is d. (iii) E(d): the probability that the final digit of a RFN is d. (iv) (a)b: the integer a reduced modulo the integer b. (v) b \a: the inte...