Abstract
In this paper, we study a generalization of Narayana’s numbers and Padovan’s numbers. This generalization also includes a sequence whose elements are Fibonacci numbers repeated three times. We give combinatorial interpretations and a graph interpretation of these numbers. In addition, we examine matrix generators and determine connections with Pascal’s triangle.
Highlights
We study a generalization of Narayana’s numbers and Padovan’s numbers
Integer sequences have always attracted the attention of many researchers, as number sequences find application in many other fields of science as well as in mathematics
We study a generalized sequence which generalize sequence of Narayana’s numbers and sequence of Padovan’s numbers, simultaneously
Summary
Integer sequences have always attracted the attention of many researchers, as number sequences find application in many other fields of science as well as in mathematics. Many generalizations and polynomials of these generalizations have been given and their properties have been studied [4,5,6, 9,10,11,12, 16]. Graduate School of Natural and Applied Sciences, Erzincan Binali Yıldırım University, The Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, al. The best known integer sequence is undoubtedly the Fibonacci sequence
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