On the arrowhead-Fibonacci numbers

Abstract

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

Keywords

• the arrowhead-fibonacci numbers
• sequence
• matrix
• period
• 11k31
• 11b50
• 11c20
• 15a15