The k-Tribonacci Matrix and the Pascal Matrix

Sri Gemawati, Musraini Musraini, Mirfaturiqa Mirfaturiqa

Abstract


This article discusses the relationship between the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn, by first constructing the k-Tribonacci matrix and then looking for its inverse. From the inverse k-Tribonacci matrix, unique characteristics can be constructed so that general shapes can be constructed, and then from the relationship of the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn obtain a new matrix, i.e. Un(k). Furthermore, a factor is derived from the relationship of the k-Tribonacci matrix Tn(k) and the Pascal matrix Pn i.e. Pn = Tn(k)Un(k).

Keywords


Tribonacci Numbers; k-Tribonacci Matrix; Pascal Matrix; Algebra of Matrix

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References


T. Koshy, “Fibonacci and Lucas Numbers with Applications, ”Wiley−Interscience, New york, 2001, doi: 10.1002/9781118033067.

M. Feinberg, “Fibonacci−tribonacci,” Fibonacci Quarterly., Vol. 1, No. 3, pp. 70-74, 1963.

R. Lather and M. Kumar, “Stability of k−tribonacci functional equation in non−Archimedean space,” International Journal of Computer Applications., Vol. 128, No. 14, pp. 27−30, 2015.

J. L. Ramirez, “Incomplete Tribonacci number and polynomials,” Journal of Integer Sequences., Vol.17, No. 14, pp. 1-13, 2014.

G. Kizilaslan, “The linear algebra of a generalized Tribonacci matrix,” Math. Stat., Vol. 72, No. 1, pp 169-181, 2023, doi: 10.31801/cfsuasmas.1052686.

R. Brawer dan M. Pirovino, “The linear algebra of the Pascal matrix, ” Linear Algebra Applications., Vol. 174, pp. 13−23, 1992, doi: 10.1016/0024-3795(92)90038-c.

R. M. Yamaleev, “Pascal matrix representation of evolution of polynomials,” International Journal Of Applied and Computational Mathematics., doi: 10.1007/s40819-015-0037-7.

N. Sabeth, S. Gemawati, and H. Saleh, “A factorization of the Tribonacci matrix and the Pascal matrix,” Applied Mathematical Sciences., Vol.11, No. 10, pp. 489−497, 2017, doi: 10.12988/ams.2017.7126.

Mirfaturiqa, S. Gemawati and M. D. H. Gamal, “Tetranacci matrix via Pascal’s matrix,” Bulletin of Mathematics., Vol. 9, No. 1, pp. 1-7, 2017.

Mirfaturiqa, Nurhasnah, and M. B. Baheramsyah, “Faktorisasi matriks Pascal dan matriks tetranacci,” Jurnal Sainstek STTPekanbaru., Vol. 11, No. 1, pp. 60-65, 2023, doi: 10.35583/js.v11i1.194.

Mirfaturiqa, Weriono, and F. Palaha, “Hubungan matriks stirling jenis kedua dengan matriks tetranacci,” Jurnal Sainstek STTPekanbaru., Vol. 11, No. 2, pp. 102-105, 2023, doi: 10.35583/js.v11i2.218.

F. Rasmi, S. Gemawati, and M. D. H. Gamal, “Relation between stirling’s numbers of the second kind and tribonacci matrix,” Bulletin of Mathematics., Vol. 10 No. 1, pp. 33-39, 2018.

Mawaddaturrohmah, S. Gemawati, and M.D.H. Gamal, “Hubungan antara matriks striling jenis kedua dan matriks k-Fibonacci,” in Prosiding Seminar Nasional STKIP PGRI Sumatera Barat, 2019, pp. 104-110.

H. Anton, Elemntary Linear Algebra , 7 Edition. Jhon Wiley & Sons, Inc, 1994.

M. Bona, A Walk Through Combinatorics, 2 Edition. USA: University of Florida Press, 2006.




DOI: https://doi.org/10.37905/jjom.v6i1.24131



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