Journal of Integer Sequences, Vol. 21 (2018), Article 18.2.5

Jacobsthal Numbers and Associated Hessenberg Matrices

Ahmet Öteleş
Department of Mathematics
Faculty of Education
Dicle University

Zekeriya Y. Karatas
Department of Mathematics, Physics and Computer Science
University of Cincinnati Blue Ash College
Blue Ash, OH 45236

Diyar O. Mustafa Zangana
Department of Mathematics
Art and Science Faculty
Siirt University


In this paper, we define two n × n Hessenberg matrices, one of which corresponds to the adjacency matrix of a bipartite graph. We then investigate the relationships between the Hessenberg matrices and the Jacobsthal numbers. Moreover, we give Maple algorithms to verify our results.

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(Concerned with sequences A000045 A000129 A001045.)

Received August 1 2017; revised versions received November 6 2017; December 25 2018; February 26 2018; March 5 2018. Published in Journal of Integer Sequences, March 6 2018.

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