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.