Some Properties of Generalized Fibonacci Sequence

摘要

For all non-negative integer n and real constants a, b,p and q, the generalized Fibonacci sequence {U_n} is defined by U_(n+2)= pU_(n+1) + qU_n with the initial values U_0= a and U_1=b . Throughout the paper, we study some properties of the generalized Fibonacci sequence. Our results will motivate some new research problems concerning the contribution of the generalized sequence.