doiSerbia

Convolutions of the generalized Jacobsthal and generalized Lucas numbers

Đorđević Gospava (Faculty of Technology, University of Niš, Leskovac, Serbia), gospava48@gmail.com
Đorđević Snežana (Faculty of Technology, University of Niš, Leskovac, Serbia), snezanadjordjevic1971@gmail.com

In this paper we consider the generalized Jacobsthal Jn,m and the generalized Jacobsthal-Lucas numbers jn,m. Also, we introduce new sequences of numbers An,m, Bn,m, Cn,m and Dn,m. Namely, these new sequences are convolutions of the sequences Jn,m and jn,m. Further, we find the generating functions and some recurrence relations for these sequences of numbers.

Keywords: recurrence relation, convolution, generating function, explicit representation, summation formula