The Hadamard-type k-step Fibonacci sequences

Abstract

In this work, we define the Hadamard-type product of two polynomials by the aid of the Hadamard product of two polynomials. Then we obtain the Hadamard-type k -step Fibonacci sequence by using Hadamard-type product of characteristic polynomials of the Fibonacci sequence and the k -step Fibonacci sequence. Also, we derive relationships between the Hadamard-type k -step Fibonacci sequences and the generating matrices for these sequences. Finally, we give some properties of these sequences such as the Binet formula, the combinatorial representations, the generating function, the exponential rep- resentation.