On the Properties of Generalized k-Pell like Sequence

The Pell sequence has been generalized in many ways, some by preserving the initial conditions, others by preserving the recurrence relation. In this paper, we define a new generalization {M_k,n}_n=1^∞, with initial conditions M_k,o = 2,M_k,1 = m + 2, which is generated by the recurrence relation M_k,n+1 = 2M_k,n + kM_k,n-1 for n ╥ 1, where k,m are integer numbers. We produce an extended Binet's formula for M_k,n and thereby the identities such as Catalan's, Simpson's, d’ Ocagene's etc.