Some binomial-sum identities for the generalized bi-periodic Fibonacci sequences

A bi-periodic sequence is a sequence which satisfies different recurrence relations depending on whether the n-th term considered is odd or even. In this paper, we investigate the properties of the generalized bi-periodic Fibonacci sequences. It is a generalization of the bi-periodic Fibonacci sequences defined by Edson and Yayenie. We derive binomial-sum identities for the generalized bi-periodic Fibonacci sequences by matrix method. Our identities generalize binomial-sum identities derived by Edson and Yayenie for the case of bi-periodic Fibonacci sequences.