24 citations · 68 across the 14 of their papers we have counts for
14 papers
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 convergents to square root of rationals
Mario Catalani
In this note we study some sequences whose ratio converges to the square root of rationals. Further we analyze some related sequences obtained when the above mentioned ratio simpli…
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…
On the average of triangular numbers
Mario Catalani
The problem we are dealing with is the following: find two sequences and such that the average of the first triangular numbers (starting with the triangular numbe…
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…