Some Identities for Balancing and Lucas-Balancing Numbers in Bidimensional Version

Several number sequences have been studied for many researchers, most of times in their unidimensional version. Our main goal is to study the bidimensional version of two sequences of known numbers. At the expense of studying the unidimensional version of the numerical balancing sequence and the numerical Lucas-balancing sequence, in particular on the basis of some of their properties, some identities related to bidimensional extensions of these two number sequences involving sums of terms are introduced: with odd index, with even index and with generic index.