Research Journal of Science and Technology

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.