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Journal articles on the topic 'Tribonacci numbers'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

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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12

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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13

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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14

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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15

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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16

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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17

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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18

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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19

Mansour, Toufik, and Mark Shattuck. "Polynomials whose coefficients are generalized Tribonacci numbers." Applied Mathematics and Computation 219, no. 15 (April 2013): 8366–74. http://dx.doi.org/10.1016/j.amc.2012.12.052.

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20

Choi, Eunmi. "A SEQUENCE OF SUMS OF TRIBONACCI NUMBERS." Far East Journal of Mathematical Sciences (FJMS) 109, no. 1 (December 20, 2018): 37–56. http://dx.doi.org/10.17654/ms109010037.

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21

Shah, Devbhadra V., and Darshana A. Mehta. "Golden proportions for the generalized Tribonacci numbers." International Journal of Mathematical Education in Science and Technology 40, no. 6 (September 15, 2009): 837–42. http://dx.doi.org/10.1080/00207390902971940.

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22

Kanovich, Max. "Multiset rewriting over Fibonacci and Tribonacci numbers." Journal of Computer and System Sciences 80, no. 6 (September 2014): 1138–51. http://dx.doi.org/10.1016/j.jcss.2014.04.006.

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23

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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24

Bednařík, Dušan, and Eva Trojovská. "Repdigits as Product of Fibonacci and Tribonacci Numbers." Mathematics 8, no. 10 (October 7, 2020): 1720. http://dx.doi.org/10.3390/math8101720.

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In this paper, we study the problem of the explicit intersection of two sequences. More specifically, we find all repdigits (i.e., numbers with only one repeated digit in its decimal expansion) which can be written as the product of a Fibonacci by a Tribonacci number (both with the same indexes). To work on this problem, our approach is to combine lower bounds from the Baker’s theory with reduction methods (based on the theory of continued fractions) due to Dujella and Pethö.

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25

Cereceda, Jose Luis. "Determinantal representations for generalized Fibonacci and tribonacci numbers." International Journal of Contemporary Mathematical Sciences 9 (2014): 269–85. http://dx.doi.org/10.12988/ijcms.2014.4323.

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26

Frontczak, Robert. "Convolutions for generalized Tribonacci numbers and related results." International Journal of Mathematical Analysis 12, no. 7 (2018): 307–24. http://dx.doi.org/10.12988/ijma.2018.8429.

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27

Trojovský, Pavel. "On Repdigits as Sums of Fibonacci and Tribonacci Numbers." Symmetry 12, no. 11 (October 26, 2020): 1774. http://dx.doi.org/10.3390/sym12111774.

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In this paper, we use Baker’s theory for nonzero linear forms in logarithms of algebraic numbers and a Baker-Davenport reduction procedure to find all repdigits (i.e., numbers with only one distinct digit in its decimal expansion, thus they can be seen as the easiest case of palindromic numbers, which are a ”symmetrical” type of numbers) that can be written in the form Fn+Tn, for some n≥1, where (Fn)n≥0 and (Tn)n≥0 are the sequences of Fibonacci and Tribonacci numbers, respectively.

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28

MERZOUK, HIND, ALI BOUSSAYOUD, and MOURAD CHELGHAM. "SYMMETRIC FUNCTIONS OF BINARY PRODUCTS OF TRIBONACCI LUCAS NUMBERS AND ORTHOGONAL POLYNOMIALS." Journal of Science and Arts 21, no. 2 (June 30, 2021): 461–78. http://dx.doi.org/10.46939/j.sci.arts-21.2-a13.

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In this paper, we will recover the new generating functions of some products of Tribonacci Lucas numbers and orthogonal polynomials. The technic used her is based on the theory of the so called symmetric functions.

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29

G\'OMEZ RUIZ, CARLOS ALEXIS, and FLORIAN LUCA. "Diophantine quadruples in the sequence of shifted Tribonacci numbers." Publicationes Mathematicae Debrecen 86, no. 3-4 (April 1, 2015): 473–91. http://dx.doi.org/10.5486/pmd.2015.7118.

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30

Irmak, Nurettin, and László Szalay. "Tribonacci Numbers Close to the Sum $2^a+3^b+5^c$." MATHEMATICA SCANDINAVICA 118, no. 1 (March 7, 2016): 27. http://dx.doi.org/10.7146/math.scand.a-23293.

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We show that there are exactly 22 solutions to the inequalities \[ 0\le T_n-2^a-3^b-5^c\le10, \] where $T_n$ denotes the $n^{\it th}$ term ($n\ge0$) of the Tribonacci sequence, and $0\le a,b\le c$ are integers. All the solutions are explicitly determined.

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31

Belovas, Igoris. "Central and Local Limit Theorems for Numbers of the Tribonacci Triangle." Mathematics 9, no. 8 (April 16, 2021): 880. http://dx.doi.org/10.3390/math9080880.

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In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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32

Bravo, Jhon J., Florian Luca, and Karina Yazan. "ON PILLAI'S PROBLEM WITH TRIBONACCI NUMBERS AND POWERS OF 2." Bulletin of the Korean Mathematical Society 54, no. 3 (May 31, 2017): 1069–80. http://dx.doi.org/10.4134/bkms.b160486.

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33

Irmak, Nurettin, and Murat Alp. "Tribonacci numbers with indices in arithmetic progression and their sums." Miskolc Mathematical Notes 14, no. 1 (2013): 125. http://dx.doi.org/10.18514/mmn.2013.523.

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34

Kafle, Bir, Florian Luca, and Alain Togbé. "x-Coordinates of Pell equations which are Tribonacci numbers II." Periodica Mathematica Hungarica 79, no. 2 (October 27, 2018): 157–67. http://dx.doi.org/10.1007/s10998-018-0264-x.

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35

Ilija, Tanackov. "Binet type formula for Tribonacci sequence with arbitrary initial numbers." Chaos, Solitons & Fractals 114 (September 2018): 63–68. http://dx.doi.org/10.1016/j.chaos.2018.06.023.

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36

Jiang, Xiaoyu, and Kicheon Hong. "Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/273680.

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Circulant matrix family is used for modeling many problems arising in solving various differential equations. The RSFPLR circulant matrices and RSLPFL circulant matrices are two special circulant matrices. The techniques used herein are based on the inverse factorization of polynomial. The exact determinants of these matrices involving Perrin, Padovan, Tribonacci, and the generalized Lucas number are given, respectively.

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37

Zhao, Feng-Zhen. "The Log-Behavior of the Partial Sum for the Tribonacci Numbers." Journal of the Indian Mathematical Society 84, no. 1-2 (January 2, 2017): 143. http://dx.doi.org/10.18311/jims/2017/6115.

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Let {T<sub>n</sub>}<sub>n</sub> ≥ 0 and {T<sub>n</sub><sup>[1]</sup>}<sub>n</sub> ≥ 0 denote the tribonacci sequence and the sequence for the partial sum of {T<sub>n</sub>}<sub>n</sub> ≥ 0, respectively. In this paper, we mainly investigate the log-concavity of T<sub>n</sub><sup>[1]</sup>}<sub>n</sub> ≥ 1 and the log-balancedness of some sequences involving T<sub>n</sub><sup>[1]</sup> . In addition, we discuss the monotonicity of some sequences related to T<sub>n</sub><sup>[1]</sup> .

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38

Luca, Florian, Amanda Montejano, Laszlo Szalay, and Alain Togbé. "On the $X$-coordinates of Pell equations which are Tribonacci numbers." Acta Arithmetica 179, no. 1 (2017): 25–35. http://dx.doi.org/10.4064/aa8553-2-2017.

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39

Bravo, Eric F., Carlos Alexis Gómez Ruiz, and Florian Luca. "X-coordinates of Pell equations as sums of two tribonacci numbers." Periodica Mathematica Hungarica 77, no. 2 (October 17, 2017): 175–90. http://dx.doi.org/10.1007/s10998-017-0226-8.

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40

Huang, Yuke, and Zhiying Wen. "The numbers of repeated palindromes in the Fibonacci and Tribonacci words." Discrete Applied Mathematics 230 (October 2017): 78–90. http://dx.doi.org/10.1016/j.dam.2017.06.012.

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41

Jiang, Zhaolin, Nuo Shen, and Juan Li. "Determinants of the RFMLR Circulant Matrices with Perrin, Padovan, Tribonacci, and the Generalized Lucas Numbers." Journal of Applied Mathematics 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/585438.

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The row first-minus-last right (RFMLR) circulant matrix and row last-minus-first left (RLMFL) circulant matrices are two special pattern matrices. By using the inverse factorization of polynomial, we give the exact formulae of determinants of the two pattern matrices involving Perrin, Padovan, Tribonacci, and the generalized Lucas sequences in terms of finite many terms of these sequences.

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42

Badidja, Salim, and Abdelmadjid Boudaoud. "Unique Representation of Positive Integers as a Sum of Distinct Tribonacci Numbers." Journal of Mathematics and Statistics 13, no. 1 (January 1, 2017): 57–61. http://dx.doi.org/10.3844/jmssp.2017.57.61.

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43

Ddamulira, Mahadi, and Florian Luca. "On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3." International Journal of Number Theory 16, no. 07 (April 9, 2020): 1643–66. http://dx.doi.org/10.1142/s1793042120500876.

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For an integer [Formula: see text], let [Formula: see text] be the [Formula: see text]-generalized Fibonacci sequence which starts with [Formula: see text] (a total of [Formula: see text] terms) and for which each term afterwards is the sum of the [Formula: see text] preceding terms. In this paper, we find all integers [Formula: see text] with at least two representations as a difference between a [Formula: see text]-generalized Fibonacci number and a power of [Formula: see text]. This paper continues the previous work of the first author for the Fibonacci numbers, and for the Tribonacci numbers.

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44

Bravo, Eric F., Carlos Alexis Gómez Ruiz, and Florian Luca. "Correction to: X-coordinates of Pell equations as sums of two Tribonacci numbers." Periodica Mathematica Hungarica 80, no. 1 (December 19, 2019): 145–46. http://dx.doi.org/10.1007/s10998-019-00305-1.

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45

Trojovský, Pavel. "On the Characteristic Polynomial of the Generalized k-Distance Tribonacci Sequences." Mathematics 8, no. 8 (August 18, 2020): 1387. http://dx.doi.org/10.3390/math8081387.

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In 2008, I. Włoch introduced a new generalization of Pell numbers. She used special initial conditions so that this sequence describes the total number of special families of subsets of the set of n integers. In this paper, we prove some results about the roots of the characteristic polynomial of this sequence, but we will consider general initial conditions. Since there are currently several types of generalizations of the Pell sequence, it is very difficult for anyone to realize what type of sequence an author really means. Thus, we will call this sequence the generalized k-distance Tribonacci sequence (Tn(k))n≥0.

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46

ASCI, MUSTAFA, and SULEYMAN AYDINYUZ. "k-ORDER FIBONACCI QUATERNIONS." Journal of Science and Arts 21, no. 1 (March 30, 2021): 29–38. http://dx.doi.org/10.46939/j.sci.arts-21.1-a04.

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In this paper, we define and study another interesting generalization of the Fibonacci quaternions is called k-order Fibonacci quaternions. Then we obtain for Fibonacci quaternions, for Tribonacci quaternions and for Tetranacci quaternions. We give generating function, the summation formula and some properties about k-order Fibonacci quaternions. Also, we identify and prove the matrix representation for k-order Fibonacci quaternions. The matrix given for k-order Fibonacci numbers is defined for k-order Fibonacci quaternions and after the matrices with the k-order Fibonacci quaternions is obtained with help of auxiliary matrices, important relationships and identities are established.

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47

Glunčić, Matko, and Ivica Martinjak. "A class of S-restricted compositions." International Journal of Number Theory 15, no. 02 (March 2019): 361–71. http://dx.doi.org/10.1142/s1793042119500180.

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In this paper, we introduce a class of restricted compositions. We prove that this class appears as a combinatorial interpretation of a generalized third-order recursive sequences. Further identities are also proved. In particular, we show that the difference of the [Formula: see text]th [Formula: see text]-tribonacci number and the sum of its three predecessors is the [Formula: see text]th regular polytopic number.

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48

Chekhova, Nataliya, Pascal Hubert, and Ali Messaoudi. "Propriétés combinatoires, ergodiques et arithmétiques de la substitution de Tribonacci." Journal de Théorie des Nombres de Bordeaux 13, no. 2 (2001): 371–94. http://dx.doi.org/10.5802/jtnb.328.

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49

Goh, William, Matthew X. He, and Paolo E. Ricci. "On the universal zero attractor of the Tribonacci-related polynomials." Calcolo 46, no. 2 (June 2009): 95–129. http://dx.doi.org/10.1007/s10092-009-0002-0.

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50

"Generalized Tribonacci Function and Tribonacci Numbers." International Journal of Recent Technology and Engineering 9, no. 1 (May 30, 2020): 1313–16. http://dx.doi.org/10.35940/ijrte.f7640.059120.

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In the language of mathematics, sequence is considered to be list of numbers arranged in a particular way. A lot of sequences have been minutely studied till date. One of the most conspicuous among them is Fibonacci sequence. It is the sequence, which can be found by adding two previous terms, where the initial conditions are 0 and 1. In a similar manner, Tribonacci sequence is also obtained by adding three previous consecutive terms. In this research paper, we introduce Tribonacci function with period s (positive integer) such that We construct some of the interesting properties, using induction technique, – odd function and - even function for Tribonacci function with period s. In the present research article we also show that exists.

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