Periodic words connected with the Tribonacci-Lucas
numbers

G. Barabash; Ya. Kholyavka; I. Tytar

doi:10.15330/ms.49.2.181-185

1. T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.

2. M. Basu, M. Das, Tribonacci matrices and a new coding theory, Discrete Math. Algorithms Appl., 6, №1, 1450008(17 pages)(1450008-1 – 1450008-17), DOI: 10.1142/ S1793830914500086.

3. W. Gerdes, Generalized tribonacci numbers and their convergent sequences, The Fibonacci Quart, 16 (1978), 269–275.

4. M. E. Waddill, Some properties of a generalized Fibonacci sequence modulo m, The Fibonacci Quart, 16 (1978), №4, 344–353.

5. N. J. A. Sloane, The online Encyclopedia of Integer sequences, Published electronically at http://oeis.org/A020992.

6. A. Vince, Period of a linear recurrence, Acta Arithmetica, 39 (1981), №4, 303–311.

7. G.Barabash, Ya.Kholyavka, I.Tytar, Periodic words connected with the Tribonacci words, Visnyk of the Lviv Univ. Series Mech. Math., 81 (2016), 5–8.

8. A. Glen, J. Justin, Episturmian words, RAIRO-Theor. Inform. Appl., 43 (2009), 403–442.

9. J.P. Duval, F. Mignosi, A. Restivo, Recurrence and periodicity in infinite words from local periods, Theoret. Comput. Sci., 262 (2001), №1–2, 269–284. doi:10.1016/S0304-3975(00)00204-8.

10. V. G. Chirskii, Arithmetic properties of polyadic series with periodic coefficients, Dokl. Math., 90 (2014), №3, 766-–768.

11. V. G. Chirskii, Arithmetic properties of polyadic series with periodic coefficients, Izvestiya: Mathematics, 81 (2017), №2, 444, 215–232. http://dx.doi.org/10.1070/IM8421.

	Periodic words connected with the Tribonacci-Lucas numbers
Author	G. Barabash¹, Ya. Kholyavka², I. Tytar³ galynabarabash71@gmail.com¹, ya_khol@ukr.net², iratytar1217@gmail.com³ 1) Ivan Franko National University of Lviv, Lviv, Ukraine; 2) Ivan Franko National University of Lviv, Lviv, Ukraine; 3) Ivan Franko National University of Lviv, Lviv, Ukraine
Abstract	We introduce periodic words that are connected with the Tribonacci-Lucas numbers and investigate their properties.
Keywords	Lucas numbers; Tribonacci numbers; Tribonacci words; polyadic numbers
DOI	doi:10.15330/ms.49.2.181-185
Reference	1. T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001. 2. M. Basu, M. Das, Tribonacci matrices and a new coding theory, Discrete Math. Algorithms Appl., 6, №1, 1450008(17 pages)(1450008-1 – 1450008-17), DOI: 10.1142/ S1793830914500086. 3. W. Gerdes, Generalized tribonacci numbers and their convergent sequences, The Fibonacci Quart, 16 (1978), 269–275. 4. M. E. Waddill, Some properties of a generalized Fibonacci sequence modulo m, The Fibonacci Quart, 16 (1978), №4, 344–353. 5. N. J. A. Sloane, The online Encyclopedia of Integer sequences, Published electronically at http://oeis.org/A020992. 6. A. Vince, Period of a linear recurrence, Acta Arithmetica, 39 (1981), №4, 303–311. 7. G.Barabash, Ya.Kholyavka, I.Tytar, Periodic words connected with the Tribonacci words, Visnyk of the Lviv Univ. Series Mech. Math., 81 (2016), 5–8. 8. A. Glen, J. Justin, Episturmian words, RAIRO-Theor. Inform. Appl., 43 (2009), 403–442. 9. J.P. Duval, F. Mignosi, A. Restivo, Recurrence and periodicity in infinite words from local periods, Theoret. Comput. Sci., 262 (2001), №1–2, 269–284. doi:10.1016/S0304-3975(00)00204-8. 10. V. G. Chirskii, Arithmetic properties of polyadic series with periodic coefficients, Dokl. Math., 90 (2014), №3, 766-–768. 11. V. G. Chirskii, Arithmetic properties of polyadic series with periodic coefficients, Izvestiya: Mathematics, 81 (2017), №2, 444, 215–232. http://dx.doi.org/10.1070/IM8421.
Pages	181-185
Volume	49
Issue	2
Year	2018
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Periodic words connected with the Tribonacci-Lucas numbers