Ömür Deveci and Anthony G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 4, Pages 589–592
DOI: 10.7546/nntdm.2022.28.4.589-592
Full paper (PDF, 693 Kb)
Details
Authors and affiliations
Ömür Deveci 
Department of Mathematics, Faculty of Science and Letters, Kafkas University
36100 Kars, Turkey
Anthony G. Shannon
Warrane College, The University of New South Wales
Kensington, NSW 2033, Australia
Abstract
In this paper, the Laplace transform and various matrix operations are applied to the characteristic polynomial of the Fibonacci numbers. From this is generated some properties of the Jacobsthal numbers, including triangles where the row sums are known sequences. In turn these produce some new properties.
Keywords
- Recurrence relations
- Laplace transform
- Fibonacci sequence
- Jacobsthal numbers
- Simson’s formula
2020 Mathematics Subject Classification
- 11B37
- 11B39
References
- Barry, P. (2003). Triangle geometry and Jacobsthal numbers. Irish Mathematical Bulletin. 51, 45–57.
- Beiler, A. H. (1966). Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. New York, Dover.
- Carlitz, L., & Riordan, J. (1964). Two element lattice permutation numbers and their q-generalization. Duke Mathematical Journal, 31, 371–388.
- Sburlati, G. (2002). Generalized Fibonacci Sequences and Linear Congruences. The Fibonacci Quarterly, 40, 446–452.
- Shannon, A. G. (2011). Some Recurrence Relations for Binary Sequence Matrices. Notes on Number Theory and Discrete Mathematics, 17(4), 9–13.
- Shapiro, L., Sprungnoli, R., Barry, P., Cheon, G.-S., He, T.-X., Merlini, D., & Wang, W. (2022). The Riordan Group and Applications. Spring, Cham.
- Sloane, N. J. A., & Plouffe, S. (1995). The Encyclopedia of Integer Sequences. San Diego, CA: Academic Press; current version available online at: https://oeis.org.
Manuscript history
- Received: 20 July 2022
- Revised: 29 September 2022
- Accepted: 3 October 2022
- Online First: 12 October 2022
Related papers
- Shannon, A. G. (2011). Some Recurrence Relations for Binary Sequence Matrices. Notes on Number Theory and Discrete Mathematics, 17(4), 9-13.
- Da Fonseca, C. M., & Shannon, A. G. (2023). On a sequence derived from the Laplace transform of the characteristic polynomial of the Fibonacci sequence. Notes on Number Theory and Discrete Mathematics, 29(3), 557-563.
Cite this paper
Deveci, Ö., & Shannon, A. G. (2022). On recurrence results from matrix transforms. Notes on Number Theory and Discrete Mathematics, 28(4), 589-592, DOI: 10.7546/nntdm.2022.28.4.589-592.
