28 research outputs found
On the self-convolution of generalized Fibonacci numbers
We focus on a family of equalities pioneered by Zhang and generalized by Zao
and Wang and hence by Mansour which involves self convolution of generalized
Fibonacci numbers. We show that all these formulas are nicely stated in only
one equation involving a bivariate ordinary generating function and we give
also a formula for the coefficients appearing in that context. As a
consequence, we give the general forms for the equalities of Zhang, Zao-Wang
and Mansour
Fibonacci–Lucas–Pell–Jacobsthal relations
In this paper, we prove several identities involving linear combinations of convolutions of the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes of second-order linearly recurrent sequences with constant coefficients. As a consequence, we obtain as special cases many identities relating exactly four sequences amongst the Fibonacci, Lucas, Pell, Pell–Lucas, Jacobsthal, and Jacobsthal–Lucas number sequences. We make use of algebraic arguments to establish our results, frequently employing the Binet-like formulas and generating functions of the corresponding sequences. Finally, our identities above may be extended so that they include only terms whose subscripts belong to a given arithmetic progression of the non-negative integers
Current Trends in Symmetric Polynomials with their Applications
This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials