Related papers: Fibonacci numbers and Trivalent graphs
In this paper, we define Tribonacci and Tribonacci-Lucas matrix sequences and investigate their properties.
The symmetric numerical semigroups S(F_a,F_b,F_c) and S(L_k,L_m,L_n) generated by three Fibonacci (F_a,F_b,F_c) and Lucas (L_k,L_m,L_n) numbers are considered. Based on divisibility properties of the Fibonacci and Lucas numbers we establish…
We present a range of difficult integration formulas involving Fibonacci and Lucas numbers and trigonometric functions. These formulas are often expressed in terms of special functions like the dilogarithm and Clausen's function. We also…
In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence…
In this paper, we give some properties of the Tribonacci and Tribonacci-Lucas quaternions and obtain some identities for them.
We establish some identities relating two sequences that are, as explained, related to the Tribonacci sequence. One of these sequences bears the same resemblance to the Tribonacci sequence as the Lucas sequence does to the Fibonacci…
Let $(F_n)_{n\ge0}$ and $(L_n)_{n\ge0}$ denote the sequences of Fibonacci and Lucas numbers respectively. This paper determines all Lucas numbers that can be represented as base $b$ mixed concatenations of a Fibonacci number and a Lucas…
In this article, we will discover some new generalized identity regarding continued fractions. We will connect the results to Fibonacci numbers and Lucas numbers. For all the proof, we will use induction.
In the first part of this paper I give an elementary overview about some number sequences which count various sorts of lattice paths in strips along the x-axis and compute their generating functions in terms of Fibonacci and Lucas…
A second order polynomial sequence is of Fibonacci type (Lucas type) if its Binet formula is similar in structure to the Binet formula for the Fibonacci (Lucas) numbers. In this paper we generalize identities from Fibonacci numbers and…
We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The method has two {\it…
We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.
This note gives an elementary exposition of a variant of the spread polynomials in terms of Fibonacci and Lucas polynomials.
Convolutions for Tribonacci numbers involving binomial coefficients are treated with ordinary generating functions and the diagonalization method of Hautus and Klarner. In this way, the relevant generating function can be established, which…
By applying the classic telescoping summation formula and its variants to identities involving inverse hyperbolic tangent functions having inverse powers of the golden ratio as arguments and employing subtle properties of the Fibonacci and…
In this paper, new families of generalized Fibonacci and Lucas numbers are introduced. In addition, we present the recurrence relations and the generating functions of the new families for $k=2$.
We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.
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…
Motivated by the resemblance of a multivariate series identity and a finite analogue of Euler's pentagonal number theorem, we study multiple extensions of the latter formula. In a different direction we derive a common extension of this…
In this work, we made a generalization that includes all bicomplex Fibonacci-like numbers such as; Fibonacci, Lucas, Pell, etc.. We named this generalization as bicomplex Horadam numbers. For bicomplex Fibonacci and Lucas numbers we gave…