On Certain Fourth-Order Linear Recursive Sequences

In this paper, we introduce a fourth-order linear recursive sequence that is related to the concept of subbalancing numbers. This sequence is constructed by using the third balancing number in the Diophantine equation of subbalancing numbers and is called the sequence of $B_3$-Lucas subbalancing numbers. Motivated by the results for $b_3$-Lucas subbalancing numbers, we obtain several algebraic identities regarding $B_3$-Lucas subbalancing numbers. Furthermore, we derive some algebraic relations between $B_3$-Lucas subbalancing numbers and some other integer sequences