On A Jacobsthal-Like Sequence Associated with KJacobsthal-Lucas Sequence

We introduce a new generalization of the known Jacobstal sequence and we call Jacobstal-Like sequence 〈Jk,n〉 and then we study on Jacobstal-Like sequence〈Jk,n〉 and kJacobsthal-Lucas sequence 〈jk,n〉 side by side by introducing two special matrices for these sequences. After that, by using these matrices we obtain Binet formula for Jacobstal-Like sequence 〈Jk,n〉 Further, we get Cassini identity for Jacobstal-Like sequence 〈Jk,n〉. Also we establish some of the interesting properties of Jacobstal-Like sequence. Then we give a limit for Jacobstal-Like sequence 〈Jk,n〉. © 2011 JCAM All rights reserved.