Algebraic properties of b_3-subbalancing and b_3-lucas subbalancing numbers

In this thesis, the subbalancing numbers obtained by an equation similar to the equation giving the balancing numbers are investigated. Algebraic identities provided by b_3-subbalancing and b_3-Lucas subbalancing numbers are obtained by making use of some theorems and equations belonging to the balancing numbers. This thesis consists of five chapters. In the first chapter, integer sequences are discussed, definitions and some algebraic properties of these integer sequences are given. In the second chapter, balancing numbers, cobalancing numbers, subbalancing numbers and b_3-subbalancing numbers are discussed. The basic definitions and theorems related to these numbers are given. In the third chapter, the sources used in writing the thesis are given. In the fourth chapter, b_3-subbalancing numbers are discussed and some algebraic equations related to these numbers are obtained. Similiar to Lucas-balancing numbers, b_3-Lucas subbalancing numbers are defined and some algebraic relations are obtained between b_3-Lucas subbalancing numbers and b_3-subbalancing numbers. In the fifth chapter, on evaluation of the results of this study is indicated.