Tribonacci and Tribonacci-Lucas Matrix Sequences with Negative Subscripts
DOI:
https://doi.org/10.26713/cma.v11i1.1103Keywords:
Tribonacci numbers, Tribonacci matrix sequence, Tribonacci-Lucas matrix sequenceAbstract
In this paper, we define Tribonacci and Tribonacci-Lucas matrix sequences with negative indices and investigate their properties.
Downloads
References
M. Akbulak and D. Bozkurt, On the order-m generalized Fibonacci k-numbers, Chaos Solitons & Fractals 42(3) (2009), 1347 – 1355, DOI: 10.1016/j.chaos.2009.03.019.
M. Basu and M. Das, Tribonacci matrices and a new coding theory, Discrete Mathematics, Algorithms and Applications 6(1) (2014), 17 pages, DOI: 10.1142/S1793830914500086.
I. Bruce, A modified Tribonacci sequence, Fibonacci Quarterly 22(3) (1984), 244 – 246.
A. C. F. Bueno, A note on generalized tribonacci sequence, Notes on Number Theory and Discrete Mathematics 21(1) (2015), 67 – 69.
G. Cerda-Morales, On the third-order Jabosthal and third-order Jabosthal-Lucas sequences and their matrix representations, arxiv:1806.03709v1 [math.CO], 2018.
H. Civciv and R. Turkmen, Notes on the (s, t)-Lucas and Lucas matrix sequences, Ars Combinatoria 89 (2008), 271 – 285.
H. Civciv and R. Turkmen, On the (s, t)-Fibonacci and Fibonacci matrix sequences, Ars Combinatoria 87 (2008), 161 – 173.
E. Duchíªne and M. Rigo, A morphic approach to combinatorial games: the tribonacci case, RAIRO – Theoretical Informatics and Applications 42(2) (2008), 375 – 393, DOI: 10.1051/ita:2007039.
M. Feinberg, Fibonacci-tribonacci, Fibonacci Quarterly 1(3) (1963), 71 – 74.
A. G. Fiorenza and G. Vincenzi, Limit of ratio of consecutive terms for general order-k linear homogeneous recurrences with constant coefficients, Chaos Solitons & Fractals 44(1-3) (2011), 147 – 152, DOI: 10.1016/j.chaos.2011.01.003.
H. H. Gulec and N. Taskara, On the (s, t)-Pell and (s, t)-Pell-Lucas sequences and their matrix representations, Applied Mathematics Letters 25 (2012), 1554 – 1559, DOI: 10.1016/j.aml.2012.01.014.
F. T. Howard and F. Saidak, Zhou's theory of constructing identities, Congress Numer. 200 (2010), 225 – 237.
L. Marohnic and T. Strmecki, Plastic number: construction and applications, Advanced Research in Scientific Areas 2012 (2012), 1523 – 1528.
A. E. Park, J. J. Fernandez, K. Schmedders and M. S. Cohen, Fibonacci sequence: relationship to the human hand, The Journal of Hand Surgery 28(1) (2002), 157 – 160, DOI: 10.1053/jhsu.2003.50000.
S. Paul and P. S. Bruckman, Solution to problem H-487 (Proposed by Stanley Rabinowitz), Fibonacci Quarterly 33 (1995), p. 382.
T. Piezas, A tale of four constants, https://sites.google.com/site/tpiezas/0012.
S. Rabinowitz, Problem H-487, Fibonacci Quarterly 32 (1994), 187.
M. Randi´c., D. A. Morales and O. Araujo, Higher-order fibonacci numbers, Journal of Mathematical Chemistry 20(1) (1996), 79 – 94, DOI: 10.1007/BF01165157.
J. N. Ridley, Packing efficiency in sunflower heads, Mathematical Biosciences 58(1) (1982), 129 – 139, DOI: 10.1016/0025-5564(82)90056-6.
A. Scott, T. Delaney and V. Hoggatt Jr., The tribonacci sequence, Fibonacci Quarterly 15(3) (1977), 193 – 200.
A. Shannon, Tribonacci numbers and Pascal's pyramid, Fibonacci Quarterly 15(3) (1977), 268 – 275.
N. J. A. Sloane, The on-line encyclopedia of integer sequences, http://oeis.org/.
Y. Soykan, Matrix sequences of tribonacci and tribonacci-Lucas numbers, arXiv:1809.07809v1 [math.NT], 2018.
W. Spickerman, Binet's formula for the Tribonacci sequence, Fibonacci Quarterly 20 (1981), 118 – 120.
K. Uslu and S. Uygun, On the (s, t) Jacobsthal and (s, t) Jacobsthal-Lucas matrix sequences, Ars Combinatoria 108 (2013), 13 – 22.
S. Uygun and K. Uslu, (s, t)-Generalized Jacobsthal matrix sequences, Springer Proceedings in Mathematics & Statistics, Computational Analysis, Amat, Ankara, May 2015, 325 – 336, DOI: 10.1007/978-3-319-28443-9_23.
S. Uygun, Some sum formulas of (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas matrix sequences, Applied Mathematics 7 (2016), 61 – 69, DOI: 10.4236/am.2016.71005.
A. A. Wani, V. H. Badshah and G. B. S. Rathore, Generalized Fibonacci and k-Pell matrix sequences, Punjab University Journal of Mathematics 50(1) (2018), 68 – 79, http://pu.edu.pk/images/journal/maths/PDF/Paper-3_51_1_2019.pdf.
C. C. Yalavigi, Properties of Tribonacci numbers, Fibonacci Quarterly 10(3) (1972), 231 – 246.
Y. Yazlik, N. Taskara, K. Uslu and N. Yilmaz, The generalized (s; t)-sequence and its matrix sequence, American Institute of Physics (AIP) Conference Proceedings 1389, 381 – 384, 2012, DOI: 10.1063/1.3636742.
V. Yegnanarayanan, The chromatic number of generalized Fibonacci prime distance graph, Journal of Mathematics and Computational Science 2(5) (2012), 1451 – 1463, http://scik.org/index.php/jmcs/article/download/434/190.
N. Yilmaz and N. Taskara, Matrix sequences in terms of Padovan and Perrin numbers, Journal of Applied Mathematics 2013 (2013), Article ID 941673, 7 pages, DOI: 10.1155/2013/941673.
N. Yilmaz and N. Taskara, On the negatively subscripted Padovan and Perrin matrix sequences, Communications in Mathematics and Applications 5(2) (2014), 59 – 72, DOI: 10.26713/cma.v5i2.227.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.