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Journal articles on the topic 'Tribonacci'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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1

Liu, Li, and Zhaolin Jiang. "Explicit Form of the Inverse Matrices of Tribonacci Circulant Type Matrices." Abstract and Applied Analysis 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/169726.

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It is a hot topic that circulant type matrices are applied to networks engineering. The determinants and inverses of Tribonacci circulant type matrices are discussed in the paper. Firstly, Tribonacci circulant type matrices are defined. In addition, we show the invertibility of Tribonacci circulant matrix and present the determinant and the inverse matrix based on constructing the transformation matrices. By utilizing the relation between left circulant,g-circulant matrices and circulant matrix, the invertibility of Tribonacci left circulant and Tribonaccig-circulant matrices is also discussed. Finally, the determinants and inverse matrices of these matrices are given, respectively.

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2

Soykan, Yüksel. "Tribonacci and Tribonacci-Lucas Sedenions." Mathematics 7, no. 1 (January 11, 2019): 74. http://dx.doi.org/10.3390/math7010074.

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The sedenions form a 16-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tribonacci and Tribonacci-Lucas sedenions. Furthermore, we present some properties of these sedenions and derive relationships between them.

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3

Tasyurdu, Yasemin. "Tribonacci and Tribonacci-Lucas hybrid numbers." International Journal of Contemporary Mathematical Sciences 14, no. 4 (2019): 245–54. http://dx.doi.org/10.12988/ijcms.2019.91124.

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4

Tasyurdu, Yasemin. "Hyperbolic Tribonacci and Tribonacci-Lucas sequences." International Journal of Mathematical Analysis 13, no. 12 (2019): 565–72. http://dx.doi.org/10.12988/ijma.2019.91167.

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5

Frontczak, Robert. "Sums of Tribonacci and Tribonacci-Lucas numbers." International Journal of Mathematical Analysis 12, no. 1 (2018): 19–24. http://dx.doi.org/10.12988/ijma.2018.712153.

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6

Vieira, Renata Passos Machado, and Francisco Regis Vieira Alves. "IDENTIDADES TRIBONACCI." Revista Sergipana de Matemática e Educação Matemática 4, no. 1 (April 27, 2019): 216–26. http://dx.doi.org/10.34179/revisem.v4i1.9823.

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O presente escrito realiza um estudo da sequência de Tribonacci, baseado no mesmo raciocínio da recorrência da Sequência de Fibonacci. Assim, foram estudadas algumas propriedades dos números inteiros positivos, dentre elas a soma dos termos da Sequência Generalizada de Tribonacci, bem como o comportamento dos termos desses números para índices negativos.

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7

Demirci, Musa, and Ismail Naci Cangul. "Tribonacci graphs." ITM Web of Conferences 34 (2020): 01002. http://dx.doi.org/10.1051/itmconf/20203401002.

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Special numbers have very important mathematical properties alongside their numerous applications in many ﬁelds of science. Probably the most important of those is the Fibonacci numbers. In this paper, we use a generalization of Fibonacci numbers called tribonacci numbers having very limited properties and relations compared to Fibonacci numbers. There is almost no result on the connections between these numbers and graphs. A graph having a degree sequence consisting of t successive tribonacci numbers is called a tribonacci graph of order t. Recently, a new graph parameter named as omega invariant has been introduced and shown to be very informative in obtaining combinatorial and topological properties of graphs. It is useful for graphs having the same degree sequence and gives some common properties of the realizations of this degree sequence together with some properties especially connectedness and cyclicness of all realizations. In this work, we determined all the tribonacci graphs of any order by means of some combinatorial results. Those results should be useful in networks with large degree sequences and cryptographic applications with special numbers.

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8

Messaoudi, A. "Tribonacci multiplication." Applied Mathematics Letters 15, no. 8 (November 2002): 981–85. http://dx.doi.org/10.1016/s0893-9659(02)00073-3.

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9

Adegoke, Kunle, Adenike Olatinwo, and Winning Oyekanmi. "New Tribonacci recurrence relations and addition formulas." Notes on Number Theory and Discrete Mathematics 26, no. 4 (November 2020): 164–72. http://dx.doi.org/10.7546/nntdm.2020.26.4.164-172.

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Only one three-term recurrence relation, namely, W_{r}=2W_{r-1}-W_{r-4}, is known for the generalized Tribonacci numbers, W_r, r\in Z, defined by W_{r}=W_{r-1}+W_{r-2}+W_{r-3} and W_{-r}=W_{-r+3}-W_{-r+2}-W_{-r+1}, where W_0, W_1 and W_2 are given, arbitrary integers, not all zero. Also, only one four-term addition formula is known for these numbers, which is W_{r + s} = T_{s - 1} W_{r - 1} + (T_{s - 1} + T_{s-2} )W_r + T_s W_{r + 1}, where ({T_r})_{r\in Z} is the Tribonacci sequence, a special case of the generalized Tribonacci sequence, with W_0 = T_0 = 0 and W_1 = W_2 = T_1 = T_2 = 1. In this paper we discover three new three-term recurrence relations and two identities from which a plethora of new addition formulas for the generalized Tribonacci numbers may be discovered. We obtain a simple relation connecting the Tribonacci numbers and the Tribonacci–Lucas numbers. Finally, we derive quadratic and cubic recurrence relations for the generalized Tribonacci numbers.

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10

Gómez Ruiz, Carlos Alexis, and Florian Luca. "Tribonacci Diophantine quadruples." Glasnik Matematicki 50, no. 1 (June 22, 2015): 17–24. http://dx.doi.org/10.3336/gm.50.1.02.

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11

Tasyurdu, Yasemin. "On the sums of Tribonacci and Tribonacci-Lucas numbers." Applied Mathematical Sciences 13, no. 24 (2019): 1201–8. http://dx.doi.org/10.12988/ams.2019.910144.

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12

BASU, MANJUSRI, and MONOJIT DAS. "TRIBONACCI MATRICES AND A NEW CODING THEORY." Discrete Mathematics, Algorithms and Applications 06, no. 01 (February 18, 2014): 1450008. http://dx.doi.org/10.1142/s1793830914500086.

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In this paper, we consider the series of Tribonacci numbers. Thereby, we introduce a new coding theory called Tribonacci coding theory based on Tribonacci numbers and show that in the simplest case, the correct ability of this method is 99.80% whereas the correct ability of the Fibonacci coding/decoding method is 93.33%.

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13

Akkus, Ilker, and Gonca Kızılaslan. "On some Properties of Tribonacci Quaternions." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 3 (December 1, 2018): 5–20. http://dx.doi.org/10.2478/auom-2018-0044.

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14

Klaška, Jiří. "Tribonacci modulo $p^t$." Mathematica Bohemica 133, no. 3 (2008): 267–88. http://dx.doi.org/10.21136/mb.2008.140617.

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15

Yilmaz, Nazmiye, and Necati Taskara. "Tribonacci and Tribonacci-Lucas numbers via the determinants of special matrices." Applied Mathematical Sciences 8 (2014): 1947–55. http://dx.doi.org/10.12988/ams.2014.4270.

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16

Badidja, Salim, Ahmed Ait Mokhtar, and Özen Özer. "Representation of integers by k-generalized Fibonacci sequences and applications in cryptography." Asian-European Journal of Mathematics 14, no. 09 (February 8, 2021): 2150157. http://dx.doi.org/10.1142/s1793557121501576.

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The aim of this paper is to construct a relation between tribonacci numbers and generalized tribonacci numbers. Besides, certain conditions are obtained to generalize the representation of a positive integer [Formula: see text] which is determined in [S. Badidja and A. Boudaoud, Representation of positive integers as a sum of distinct tribonacci numbers, J. Math. Statistic. 13 (2017) 57–61] for a [Formula: see text]-generalized Fibonacci numbers [Formula: see text]. Lastly, some applications to cryptography are given by using [Formula: see text].

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17

Magnani, Kodjo Essonana. "On Third-Order Linear Recurrent Functions." Discrete Dynamics in Nature and Society 2019 (March 26, 2019): 1–4. http://dx.doi.org/10.1155/2019/9489437.

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A function ψ:R→R is said to be a Tribonacci function with period p if ψ(x+3p)=ψ(x+2p)+ψ(x+p)+ψ(x), for all x∈R. In this paper, we present some properties on the Tribonacci functions with period p. We show that if ψ is a Tribonacci function with period p, then limx→∞ψ(x+p)/ψ(x)=β, where β is the root of the equation x3-x2-x-1=0 such that 1<β<2.

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18

Sellami, T. "On the Tribonacci fractals." International Journal of Scientific Research in Mathematical and Statistical Sciences 5, no. 2 (April 30, 2018): 70–74. http://dx.doi.org/10.26438/ijsrmss/v5i2.7074.

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19

Choi, Eunmi, and Jiin Jo. "IDENTITIES INVOLVING TRIBONACCI NUMBERS." Journal of the Chungcheong Mathematical Society 28, no. 1 (February 15, 2015): 39–51. http://dx.doi.org/10.14403/jcms.2015.28.1.39.

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20

Phadte, C. N., and Y. S. Valaulikar. "On Pseudo Tribonacci Sequence." International Journal of Mathematics Trends and Technology 31, no. 3 (March 25, 2016): 195–200. http://dx.doi.org/10.14445/22315373/ijmtt-v31p526.

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21

Choi, Eunmi, and Jiin Jo. "On Partial Sum of Tribonacci Numbers." International Journal of Mathematics and Mathematical Sciences 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/301814.

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We study the sumst(k,r)=∑i=0tTki+rofkstep apart Tribonacci numbers for any1≤r≤k. We prove thatst(k,r)satisfies certain Tribonacci rulest(k,r)=akst-1(k,r)+bkst-2(k,r)+st-3(k,r)+λwith integersak,bk,ck, andλ.

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22

Haryanto, Loeky, Rahmaniah Rakhman, and Arnensih Alimuddin. "Generalisasi Permainan Wythoff ke Permainan Tribonacci." Jurnal Matematika Statistika dan Komputasi 14, no. 1 (February 11, 2018): 100. http://dx.doi.org/10.20956/jmsk.v14i1.3546.

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Kata fibonacci bisa diturunkan dengan menggunakan suatu iterasi morfisma pada monoid {a, b}*. Dengan mengidentifikasi posisi kedua huruf a dan b di dalam kata fibonacci, diperoleh barisan (an, bn)n³0 yang membentuk posisi-P dari permainan Wythoff. Demikian pula, kata tribonacci bisa diturunkan dengan menggunakan suatu iterasi morfisma pada monoid {a, b, c}*. Dengan mengidentifikasi ketiga huruf a, b dan c di dalam kata tribonacci, diperoleh barisan (An, Bn, Cn)n³0 yang membentuk posisi-P dari suatu permainan yang ditulis oleh [2] dan diberi nama: permainan tribonacci. Selain menggunakan morfisma, kedua barisan (an, bn)n³0 dan (An, Bn, Cn)n³0 bisa dikonstruksi secara rekursif dengan menggunakan operator Mex (Minimum excluded). Berdasarkan parameterdan persyaratan yang digunakan pada kedua konstruksi, disimpulkan bahwa barisan (An, Bn, Cn)n³0 merupakan perluasan dari barisan urutan-2 (an, bn)n³0. Tetapi ada masalah perluasan cara konstruksi posisi-P permainan Wythoff berdasarkan barisan Beatty ke cara yang serupa untuk konstruksi posisi-P permainan tribonacci.

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23

Kızılateş, Can, Paula Catarino, and Naim Tuğlu. "On the Bicomplex Generalized Tribonacci Quaternions." Mathematics 7, no. 1 (January 14, 2019): 80. http://dx.doi.org/10.3390/math7010080.

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In this paper, we introduce the bicomplex generalized tribonacci quaternions. Furthermore, Binet’s formula, generating functions, and the summation formula for this type of quaternion are given. Lastly, as an application, we present the determinant of a special matrix, and we show that the determinant is equal to the n th term of the bicomplex generalized tribonacci quaternions.

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24

Bravo, Eric F., and Jhon J. Bravo. "Tribonacci numbers with two blocks of repdigits." Mathematica Slovaca 71, no. 2 (April 1, 2021): 267–74. http://dx.doi.org/10.1515/ms-2017-0466.

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Abstract The Tribonacci sequence is a generalization of the Fibonacci sequence which starts with 0,0,1 and each term afterwards is the sum of the three preceding terms. Here, we show that the only Tribonacci numbers that are concatenations of two repdigits are 13,24,44,81. This paper continues a previous work that searched for Fibonacci numbers which are concatenations of two repdigits.

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25

Yaying, Taja, and Bipan Hazarika. "On sequence spaces defined by the domain of a regular tribonacci matrix." Mathematica Slovaca 70, no. 3 (June 25, 2020): 697–706. http://dx.doi.org/10.1515/ms-2017-0383.

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AbstractIn this article we introduce Tribonacci sequence spaces ℓp(T) (1 ≤ p ≤ ∞) derived by the domain of a newly defined regular Tribonacci matrix. We give some topological properties, inclusion relation, obtain the Schauder basis and determine the α-, β- and γ-duals of the new spaces. We characterize the matrix classes on ℓp(T). Finally, we give some geometric properties of the space ℓp(T).

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26

Kuhapatanakul, Kantaphon, and Lalitphat Sukruan. "n-tribonacci triangles and applications." International Journal of Mathematical Education in Science and Technology 45, no. 7 (March 7, 2014): 1068–75. http://dx.doi.org/10.1080/0020739x.2014.892164.

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27

Klaška, Jiří. "Tribonacci partition formulas modulo m." Acta Mathematica Sinica, English Series 26, no. 3 (February 15, 2010): 465–76. http://dx.doi.org/10.1007/s10114-010-8433-8.

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28

Li, Juan, Zhaolin Jiang, and Fuliang Lu. "Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/381829.

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Circulant matrices play an important role in solving ordinary and partial differential equations. In this paper, by using the inverse factorization of polynomial of degreen, the explicit determinants of circulant and left circulant matrix involving Tribonacci numbers or generalized Lucas numbers are expressed in terms of Tribonacci numbers and generalized Lucas numbers only. Furthermore, four kinds of norms and bounds for the spread of these matrices are given, respectively.

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29

Klaška, Jiří. "Tribonacci modulo $2^t$ and $11^t$." Mathematica Bohemica 133, no. 4 (2008): 377–87. http://dx.doi.org/10.21136/mb.2008.140627.

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30

Cerda-Morales, Gamaliel. "Quadratic approximation of generalized Tribonacci sequences." Discussiones Mathematicae - General Algebra and Applications 38, no. 2 (2018): 227. http://dx.doi.org/10.7151/dmgaa.1288.

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31

Bravo, Eric F., Carlos A. Gómez, and Florian Luca. "Total multiplicity of the Tribonacci sequence." Colloquium Mathematicum 159, no. 1 (2020): 71–76. http://dx.doi.org/10.4064/cm7730-2-2019.

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32

Atanassova, Lilija. "A remark on the Tribonacci sequences." Notes on Number Theory and Discrete Mathematics 25, no. 3 (September 30, 2019): 138–41. http://dx.doi.org/10.7546/nntdm.2019.25.3.138-141.

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33

Choi, Eunmi. "MODULAR TRIBONACCI NUMBERS BY MATRIX METHOD." Pure and Applied Mathematics 20, no. 3 (August 31, 2013): 207–21. http://dx.doi.org/10.7468/jksmeb.2013.20.3.207.

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34

Szynal-Liana, Anetta, and Iwona Włoch. "Some properties of generalized Tribonacci quaternions." Scientific Issues Jan Długosz University in Częstochowa. Mathematics 22 (2017): 73–81. http://dx.doi.org/10.16926/m.2017.22.06.

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35

Gao, Yating, Wenlong Huang, and Shaohua Tao. "The phase-only Tribonacci photon sieve." Optics Communications 474 (November 2020): 126090. http://dx.doi.org/10.1016/j.optcom.2020.126090.

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36

Cereceda, José Luis. "Binet's formula for generalized tribonacci numbers." International Journal of Mathematical Education in Science and Technology 46, no. 8 (April 10, 2015): 1235–43. http://dx.doi.org/10.1080/0020739x.2015.1031837.

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37

Choi, EunMi. "ON MODULAR FIBONACCI AND TRIBONACCI TABLES." Journal of the Chungcheong Mathematical Society 26, no. 3 (August 15, 2013): 577–90. http://dx.doi.org/10.14403/jcms.2013.26.3.577.

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38

Gómez Ruiz, Carlos Alexis, and Florian Luca. "Multiplicatively dependent triples of Tribonacci numbers." Acta Arithmetica 171, no. 4 (2015): 327–53. http://dx.doi.org/10.4064/aa171-4-3.

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39

Pankaj. "Determinantal Identities of k-Tribonacci Sequences." Research Journal of Science and Technology 10, no. 3 (2018): 197. http://dx.doi.org/10.5958/2349-2988.2018.00027.x.

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40

Tan, Bo, and Zhi-Ying Wen. "Some properties of the Tribonacci sequence." European Journal of Combinatorics 28, no. 6 (August 2007): 1703–19. http://dx.doi.org/10.1016/j.ejc.2006.07.007.

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41

Yilmaz, Nazmiye, and Necati Taskara. "Incomplete Tribonacci–Lucas Numbers and Polynomials." Advances in Applied Clifford Algebras 25, no. 3 (December 21, 2014): 741–53. http://dx.doi.org/10.1007/s00006-014-0523-8.

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42

Rybołowicz, Bernard, and Agnieszka Tereszkiewicz. "Generalized tricobsthal and generalized tribonacci polynomials." Applied Mathematics and Computation 325 (May 2018): 297–308. http://dx.doi.org/10.1016/j.amc.2017.12.042.

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43

Khan, Vakeel A., Izhar Ali Khan, SK Ashadul Rahaman, and Ayaz Ahmad. "On Tribonacci I -convergent sequence spaces." Journal of Mathematics and Computer Science 24, no. 03 (February 27, 2021): 225–34. http://dx.doi.org/10.22436/jmcs.024.03.04.

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44

Chen, Kuo-Jye. "A simple proof of an identity of Pethe and Horadam." Bulletin of the Australian Mathematical Society 50, no. 1 (August 1994): 117–21. http://dx.doi.org/10.1017/s000497270000962x.

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45

Evink, Tim, and Paul Alexander Helminck. "Tribonacci numbers and primes of the form p = x2 + 11y2." Mathematica Slovaca 69, no. 3 (June 26, 2019): 521–32. http://dx.doi.org/10.1515/ms-2017-0244.

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Abstract In this paper we show that for any prime number p not equal to 11 or 19, the Tribonacci number Tp−1 is divisible by p if and only if p is of the form x2 + 11y2. We first use class field theory on the Galois closure of the number field corresponding to the polynomial x3 − x2 − x − 1 to give the splitting behavior of primes in this number field. After that, we apply these results to the explicit exponential formula for Tp−1. We also give a connection between the Tribonacci numbers and the Fourier coefficients of the unique newform of weight 2 and level 11.

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46

Chim, Kwok Chi, István Pink, and Volker Ziegler. "On a variant of Pillai’s problem." International Journal of Number Theory 13, no. 07 (February 2017): 1711–27. http://dx.doi.org/10.1142/s1793042117500981.

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47

Yagmur, T\"{u}lay. "A note on generalized hybrid Tribonacci numbers." Discussiones Mathematicae - General Algebra and Applications 40, no. 2 (2020): 187. http://dx.doi.org/10.7151/dmgaa.1343.

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48

Zhou, Shujie, and Li Chen. "Tribonacci Numbers and Some Related Interesting Identities." Symmetry 11, no. 10 (September 24, 2019): 1195. http://dx.doi.org/10.3390/sym11101195.

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The main purpose of this paper is, by using elementary methods and symmetry properties of the summation procedures, to study the computational problem of a certain power series related to the Tribonacci numbers, and to give some interesting identities for these numbers.

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49

Frontczak, Robert. "Relations for generalized Fibonacci and Tribonacci sequences." Notes on Number Theory and Discrete Mathematics 25, no. 1 (March 2019): 178–92. http://dx.doi.org/10.7546/nntdm.2019.25.1.178-192.

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50

Sirvent, Víctor F. "The common dynamics of the Tribonacci substitutions." Bulletin of the Belgian Mathematical Society - Simon Stevin 7, no. 4 (2000): 571–82. http://dx.doi.org/10.36045/bbms/1103055617.

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