Abstract
In this paper, we introduce the generalized 5-primes numbers sequences and we deal with, in detail, three special cases which we call them 5-primes, Lucas 5-primes and modified 5-primes sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences ........................... .................... ....................................
2010 Mathematics Subject Classication. 11B39, 11B83.
Keywords
5-primes numbers Lucas 5-primes numbers generalized Pentanacci numbers modied 5-primes numbers
References
- [1] Howard, F.T., Saidak, F., Zhou’s Theory of Constructing Identities, Congress Numer. 200, 225-237, 2010.
- [2] Kalman, D., Generalized Fibonacci Numbers By Matrix Methods, Fibonacci Quarterly, 20(1), 73-76, 1982.
- [3] Kiliç, E., Stanica, P., A Matrix Approach for General Higher Order Linear Recurrences, Bulletin of the Malaysian Mathematical Sciences Society, (2) 34(1), 51.67, 2011.
- [4] Melham, R. S., Some Analogs of the Identity , F_n^2+F_(n+1)^2=F_(2n+1)^2 Fibonacci Quarterly, 305-311, 1999.
- [5] Natividad, L. R., On Solving Fibonacci-Like Sequences of Fourth, Fifth and Sixth Order, International Journal of Mathematics and Computing, 3 (2), 2013.
- [6] Rathore, G.P.S., Sikhwal, O., Choudhary, R., Formula for finding nth Term of Fibonacci-Like Sequence of Higher Order, International Journal of Mathematics And its Applications, 4 (2-D), 75-80, 2016.
- [7] Sloane, N.J.A., The on-line encyclopedia of integer sequences, http://oeis.org/
- [8] Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2), 45-56, 2019.
- [9] Soykan, Y., Sum Formulas For Generalized Fifth-Order Linear Recurrence Sequences, Journal of Advances in Mathematics and Computer Science, 34(5), 1-14, 2019, Article no.JAMCS.53303, ISSN: 2456-9968, DOI: 10.9734/JAMCS/2019/v34i530224.
Abstract
References
- [1] Howard, F.T., Saidak, F., Zhou’s Theory of Constructing Identities, Congress Numer. 200, 225-237, 2010.
- [2] Kalman, D., Generalized Fibonacci Numbers By Matrix Methods, Fibonacci Quarterly, 20(1), 73-76, 1982.
- [3] Kiliç, E., Stanica, P., A Matrix Approach for General Higher Order Linear Recurrences, Bulletin of the Malaysian Mathematical Sciences Society, (2) 34(1), 51.67, 2011.
- [4] Melham, R. S., Some Analogs of the Identity , F_n^2+F_(n+1)^2=F_(2n+1)^2 Fibonacci Quarterly, 305-311, 1999.
- [5] Natividad, L. R., On Solving Fibonacci-Like Sequences of Fourth, Fifth and Sixth Order, International Journal of Mathematics and Computing, 3 (2), 2013.
- [6] Rathore, G.P.S., Sikhwal, O., Choudhary, R., Formula for finding nth Term of Fibonacci-Like Sequence of Higher Order, International Journal of Mathematics And its Applications, 4 (2-D), 75-80, 2016.
- [7] Sloane, N.J.A., The on-line encyclopedia of integer sequences, http://oeis.org/
- [8] Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, Int. J. Adv. Appl. Math. and Mech. 7(2), 45-56, 2019.
- [9] Soykan, Y., Sum Formulas For Generalized Fifth-Order Linear Recurrence Sequences, Journal of Advances in Mathematics and Computer Science, 34(5), 1-14, 2019, Article no.JAMCS.53303, ISSN: 2456-9968, DOI: 10.9734/JAMCS/2019/v34i530224.
Details
| Primary Language | English |
|---|---|
| Journal Section | Basic Sciences and Engineering |
| Authors | |
| Publication Date | August 19, 2020 |
| Published in Issue | Year 2020 Volume: 4 Issue: 3 |
