Determinantal forms and recursive relations of the Delannoy two-functional sequence

Open Access

Original research article

Author(s):

Feng Qi^a, Muhammet Cihat Dağlı^b, Wei-Shih Du^c

^aCollege of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia, China;
School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin 300387, China;
Institute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan, China
^bDepartment of Mathematics, Akdeniz University, 07058-Antalya, Turkey
^cDepartment of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan

Advances in the Theory of Nonlinear Analysis and its Applications 4(3), 184-193.

Received: July 21, 2020

Accepted: August 29, 2020

Published: August 31, 2020

Abstract

In this paper, the authors establish closed forms for the Delannoy two-functional sequence and its difference in terms of the Hessenberg determinants. Recursive relations for the Delannoy two-functional sequence and its difference are derived, and closed forms are deduced in terms of the Hessenberg determinants and recursive relations for the Delannoy one-functional sequence, the Delannoy numbers, and central Delannoy numbers.

Keywords: closed form, recursive relation, difference, Hessenberg determinant, Delannoy two-functional sequence, Delannoy one-functional sequence, Delannoy number, central Delannoy number.

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APA Style

Qi, F., Dağlı, M. C., & Du, W. S. (2020). Determinantal forms and recursive relations of the Delannoy two-functional sequence. Advances in the Theory of Nonlinear Analysis and its Application, 4(3), 184-193.