A Note on Binomial Transform of the Generalized 3-primes Sequence


  • Yüksel Soykan Zonguldak Bülent Ecevit University


generalized Tribonacci sequence., Lucas 3-primes sequence, 3-primes sequence, binomial transform


In this paper, we define the binomial transform of the generalized 3-primes sequence and as special cases, the binomial transform of the 3-primes, Lucas 3-primes, modified 3-primes sequences will be introduced. We investigate their properties in details.


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Barry, P., On Integer-Sequence-Based Cnstructions of Gneralized Pascal Triangles, Journal of Integer Sequences 9, Article 06.2.4, 2006.

Bhadouria, P., Jhala, D., Singh, B., Binomial Transforms of the k-Lucas Sequences and its Properties, J. Math. Computer Sci., 8, 81-92, 2014.

Bruce, I., A modified Tribonacci Sequence, The Fibonacci Quarterly, 22 (3), 244–246, 1984.

Catalani, M., Identities for Tribonacci-Related Sequences - arXiv preprint, https://arxiv.org/pdf/math/0209179.pdf math/0209179, 2002.

Choi, E., Modular Tribonacci Numbers by Matrix Method, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math 20 (3), 207–221, 2013. https://doi.org/10.7468/jksmeb.2013.20.3.207

Elia, M., Derived Sequences, The Tribonacci Recurrence and Cubic Forms, The Fibonacci Quarterly, 39 (2), 107-115, 2001.

Er, M. C., Sums of Fibonacci Numbers by Matrix Methods, Fibonacci Quart. 22(3), 204-207, 1984.

Falcón, S., Binomial Transform of the Generalized k-Fibonacci Numbers, Communications in Mathematics and Applications, 10(3), 643–651, 2019. DOI: 10.26713/cma.v10i3.1221

Gould, H. W., Series Transformations for Finding Recurrences for Sequences, The Fibonacci Quarterly 28(2), 166-171, 1990.

Haukkanen, P., Formal Power Series for Binomial Sums of Sequences of Numbers, The Fibonacci Quarterly, 31(1), 28-31, 1993.

Howard, F.T., Saidak, F., Zhou’s Theory of Constructing Identities, Congress Numer. 200, 225-237, 2010.

Kalman, D., Generalized Fibonacci Numbers By Matrix Methods, Fibonacci Quart., 20(1), 73-76, 1982.

Kaplan, F., Arzu Özkoç Öztürk, A.Ö., On the Binomial Transforms of the Horadam Quaternion Sequences, Authorea. December 08, 2020. DOI: .22541/au.160743179.90770528/v1

Kızılates, C., Tuglu, N., Çekim, B., Binomial Transform of Quadrapell Sequences and Quadrapell Matrix Sequences, Journal of Science and Arts, 1(38), 69-80, 2017.

Knuth., D. E., The Art of Computer Programming 3. Reading, MA: Addison Wesley, 1973.

Kwon, Y., Binomial Transforms of the Modified k-Fibonacci-like Sequence, International Journal of Mathematics and Computer Science, 14(1), 47-59, 2019.

Lin, P. Y., De Moivre-Type Identities For The Tribonacci Numbers, The Fibonacci Quarterly, 26, 131-134, 1988.

Pethe, S., Some Identities for Tribonacci sequences, The Fibonacci Quarterly, 26 (2), 144–151, 1988.

Prodinger, H., Some Information about the Binomial Transform, The Fibonacci Quarterly 32.5, 412-15, 1994.

Scott, A., Delaney, T., Hoggatt Jr., V., The Tribonacci Sequence, The Fibonacci Quarterly, 15 (3), 193–200, 1977.

Shannon, A., Tribonacci Numbers and Pascal’s Pyramid, The Fibonacci Quarterly, 15 (3), pp. 268 and 275, 1977.

Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2),

-56, 2019 (ISSN: 2347-2529).

Soykan, Y. Tribonacci and Tribonacci-Lucas Sedenions. Mathematics 7 (1), 74, 2019.


Soykan, Y., Summing Formulas For Generalized Tribonacci Numbers, Universal Journal of Mathematics and Applications, 3(1), 1-11, 2020. DOI: https://doi.org/10.32323/ujma.637876

Soykan Y., Generalized Tribonacci Numbers: Summing Formulas, Int. J. Adv. Appl. Math. and Mech. 7(3), 57-76,2020.

Soykan, Y., A Closed Formula for the Sums of Squares of Generalized Tribonacci numbers, Journal of in Mathematics, 16(2), 2932-2941, 2020.

Soykan, Y., On the Sums of Squares of Generalized Tribonacci Numbers: Closed Formulas of Pn k=0 xkW2 k , Archives

of Current Research International, 20(4), 22-47, 2020. DOI: 10.9734/ACRI/2020/v20i430187

Soykan, Y., On Generalized Grahaml Numbers, Journal of Advances in Mathematics and Computer Science, 35(2), 42-57, 2020. DOI: 10.9734/JAMCS/2020/v35i230248.

Soykan, Y., Binomial Transform of the Generalized Tribonacci Sequence, Asian Research Journal of Mathematics, 16(10), 26-55, 2020.DOI: 10.9734/ARJOM/2020/v16i1030229

Spickerman, W., Binet’s Formula for the Tribonacci Sequence, The Fibonacci Quarterly, 20, 118–120, 1982.

Spivey, M. Z., Combinatorial Sums and Finite Differences, Discrete Math. 307, 3130–3146, 2007. https://doi.org/10.1016/j.disc.2007.03.052

Yalavigi, C. C., Properties of Tribonacci Numbers, The Fibonacci Quarterly, 10 (3), 231–246, 1972.

Uygun, S., Erdogdu, A., Binomial Transforms k-Jacobsthal Sequences, J. Math. Comput. Sci. 7(6), 1100-1114, 2017. https://doi.org/10.28919/jmcs/3474

Uygun, S., The Binomial Transforms of the Generalized (s,t)-Jacobsthal Matrix Sequence, International Journal ofAdvances in Applied Mathematics and Mechanics, 6(3), 14-20, 2019.

Yilmaz, N., Taskara, N., Binomial Transforms of the Padovan and Perrin Matrix Sequences, Abstract and Applied Analysis, Volume 2013, Article ID 497418, 7 pages, 2013. http://dx.doi.org/10.1155/2013/497418




How to Cite

Soykan, Y. (2020). A Note on Binomial Transform of the Generalized 3-primes Sequence. MathLAB Journal, 7, 168-190. Retrieved from https://purkh.com/index.php/mathlab/article/view/960



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