Matrix generators of Pell sequences

ivMATRIX GENERATORS OF PELL SEQUENCES(M.Sc. Thesis)Selcan EK‹C‹GAZI UNIVERSITYINSTITUTE OF SCIENCE AND TECHNOLOGYJanuary 2006ABSTRACTIn this article, by the help of general series {Un} which is definedrecursively by Un+2 = b Un+1 + Un , U0 = 0, U1 = 1, some of the propertiesof Fibonacci and Pell sequences are obtained by the use of generatorb1matrix B = = G.10First we determine a closed form expression of the entries aij of anyfunction f(B) = A = [aij] based on a polynomial representation of thefunction itself.Then we consider a set of functions f such that f(B) can be found bymeans of a power series expansion  = [âij] = f(B) and equate aij ve âij forsome i and j, thus getting one or more Pell and Fibonacci-type identities.Science Code : 204.1.025Key Words : Pell sequences, Fibonacci sequencesPage Number : 55Advisor : Prof. Dr. Dursun TA CI