24 citations · 68 across the 14 of their papers we have counts for
9 papers · 1 filter
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…
Sampling from a couple of negatively correlated gamma variates
Mario Catalani
We propose two algorithms for sampling from two gamma variates possessing a negative correlation. The case of positive correlation is easily solved, so we just mention it. The main…
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…
A particular matrix and its relationships with Fibonacci numbers
Mario Catalani
Determinants and symmetric functions of the eigenvalues of matrices characterizing stochastic processes with indepedent increments. Relationships with Fibonacci numbers are derived…
Identities for Tribonacci-related sequences
Mario Catalani
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…