Factorizations and representations of second order linear recurrences with indices in arithmetic progressions
type: Item
instance of: scholarly article
title: Factorizations and representations of second order linear recurrences with indices in arithmetic progressions
zbMATH Open document ID: 1246.11034
author: Emrah Kılıç
author: Pantelimon Stanica
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2011-07-06T00:00:00Z
review text: Let \(\{V_n\}\) and \(\{U_n\}\) be generalized Lucas and Fibonacci sequences satisfying a general second order linear recurrence relation with Lucas and Fibonacci type initial conditions. The authors find second order linear recurrences for the sequences \(\{V_{\pm kn}\}\) and \(\{U_{\pm kn}\}\). Using these recurrence relations, the authors show that the members of these sequences are the determinants of certain tridiagonal matrices. Further, the authors present representations and trigonometric factorizations of the members of these sequences applying matrix methods and methods relying on Chebyshev polynomials of the first and second kinds. The authors also give the generating functions and some combinatorial representations of these sequences.
reviewed by: Pentti Haukkanen
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 11C20
zbMATH DE Number: 5917660
zbMATH Keywords: generalized Lucas and Fibonacci numbers
zbMATH Keywords: second order linear recurrence sequences
zbMATH Keywords: trigonometric factorizations
zbMATH Keywords: determinants
zbMATH Keywords: tridiagonal matrices
zbMATH Keywords: generating functions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5917660