Characterization of generalized order-k pell numbers

vCHARACTERIZATION OF GENERALIZED ORDER-k PELL NUMBERS(Ph.D. Thesis)Emrah KILIÇGAZİ UNIVERSITYINSTITUTE OF SCIENCE AND TECHNOLOGYSeptember 2006ABSTRACTIn this study, using the Pell numbers, the generalized order-k Pell numberswere defined and using this definition, the generating matrix for thegeneralized order-k Pell numbers was obtained. Also a method for the sumsof the generalized order-k Pell numbers by matrix methods was given. Thegeneralized Binet Formula for the generalized Pell numbers given for thewell known Binet formula for the usual Pell numbers was obtained. Finally,the generating function, exponential and combinatorial representations ofthe generalized order-k Pell numbers were characterized.Science Code : 204.1.025Key Words : Generalized order-k Pell number, matrix methods,generalized Binet formula, generating functionPage Number : 47Adviser : Prof. Dr. Dursun TAŞCI