Mersene, Jacobstahl, and Jacobstahl-Lucas numbers with negative subscripts

Abstract

In this paper, we present the usual Mersenne, Jacobsthal and Jacobsthal-Lucas numbers with negative subscripts. Furthermore, we get many identities ofthese sequences such as Gelin-Cesaro identity and d'Ocagne's identity and certainformulas for computing the sums of their terms. In addition, we give the generatingmatrices of these sequences. We also that their sums can be obtained by employingmatrix technique.