Some Identities for the (a, b; k)-Nacci Sequences

Abstract

In this paper, we introduce a generalization of the k-generalized Fibonacci sequence, called the (a, b; k)-nacci sequence, where a and b are real numbers and k ≥ 2 is an integer. The (a, b; k)-nacci sequence is defined recursively as follows:

        We also provide some identities involving the sum of the (a, b; k)-nacci terms and investigate the sums of the squares of the (a, b; k)-nacci numbers.