On subbalancing numbers involving the third balancing number in the Diophantine equation

In this paper, we consider subbalancing numbers formed by using the third balancing number in the Diophantine equation. We obtain some algebraic identities on these numbers which are also known as $B_3$-subbalancing numbers. We provide a variety of sum formulas and some divisibility properties associated with these numbers. We also give several Pythagorean triples obtained by using $B_3$-subbalancing numbers. Furthermore, we derive some functions that takes $B_3$-subbalancing and balancing numbers values for $B_3$-subbalancing number arguments.