On the arrowhead-Fibonacci numbers

In this paper, we define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of the -step Fibonacci sequence and then we give some of their properties. Also, we study the arrowhead-Fibonacci sequence modulo and we obtain the cyclic groups from the generating matrix of the arrowhead-Fibonacci numbers when read modulo . Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the arrowhead-Fibonacci sequence modulo