24 citations · 68 across the 14 of their papers we have counts for
8 papers · 1 filter
Identities for Fibonacci and Lucas polynomials derived from a book of Gould
Mario Catalani
This note is dedicated to Professor Gould. The aim is to show how the identities in his book "Combinatorial Identities" can be used to obtain identities for Fibonacci and Lucas pol…
Some formulae for bivariate Fibonacci and Lucas polynomials
Mario Catalani
We derive a collection of identities for bivariate Fibonacci and Lucas polynomials using essentially a matrix approach as well as properties of such polynomials when the variables…
Sequences related to the Pell generalized equation
Mario Catalani
We consider sequences of the type ( and integers) and show that all sequences that solve particular cases of the Pell generalized equati…
Generalized bivariate Fibonacci polynomials
Mario Catalani
We define generalized bivariate polynomials, from which upon specification of initial conditions the bivariate Fibonacci and Lucas polynomials are obtained. Using essentially a mat…
Polymatrix and generalized polynacci numbers
Mario Catalani
We consider -th order linear recurrences that can be thought of as generalizations of the Lucas sequence. We exploit some interplay with matrices that again can be considered ge…
On the roots of the cubic defining the Tribonacci sequences
Mario Catalani
We consider a sequence of sums of powers of the the roots of the cubic equation characterizing the Tribonacci sequences and derive its relationship with a particular Tribonacci seq…