On the generalized Fibonacci like sequences and matrices

In this paper, we study the generalized Fibonacci like sequences {tk,n}k is an element of{2,3},n is an element of N with arbitrary initial seed and give some new and wellknown identities like Binet's formula, trace sequence, Catalan's identity, generating function, etc. Further, we study various properties of these generalized sequences, establish a recursive matrix and relationships with Fibonacci and Lucas numbers and sequence of Fibonacci traces. In this study, we examine the nature of identities and recursive matrices for arbitrary initial values.