The arrowhead-fibonacci-random-type sequences

Abstract

In this paper, we define the arrowhead-Fibonacci-random-type sequence and the arrowhead-Padovan-random-type sequence which is a special form of the arrowhead-Fibonacci-random-type se-quence.Then we obtain the Binet formula for the arrow head-Padovan-random-type sequence.Also, we give the permanental and the deter-minantal representations of the arrowhead-Fibonacci-random-type sequence. Finally, we derive the combinatorial representations, the exponential representations and the sums of the arrowhead-Fibonacci-random-type numbers by the aid of the generating function and the generating matrix of the arrowhead-Fibonacci-random-type sequence. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.