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Year 2021, , 25 - 43, 30.06.2021
https://doi.org/10.47000/tjmcs.787578

Abstract

Thanks

Makalemizi inceleyen, değerlendiren editörümüze ve hakemlerimize teşekkür ederiz.

References

  • [1] Asci, M., Gurel E., Gaussian Jacobsthal and Gaussian Jacobsthal Polynomials, Notes on Number Theory and Discrete Mathematics, 19(2013), 25-36.
  • [2] Bacani, J. B., Rabago, J. F. T., On Generalized Fibonacci Numbers, Applied Mathematical Sciences,9(25)(2015), 3611-3622.
  • [3] Berzsenyi, G., Gaussian Fibonacci Numbers, Fibonacci Quarterly, 15(3)(1977), 233-236.
  • [4] Catarino, P., Campos, H., A note on Gaussian Modified Pell numbers, Journal of Information & Optimization Sciences, 39(6)(2018), 1363- 1371.
  • [5] Dresden, G. P., Du, Z., A Simplified Binet Formula for k-Generalized Fibonacci Numbers, Journal of Integer Sequences, 17(4)(2014), 1-9.
  • [6] Fraleigh, J. B., A First Course In Abstract Algebra, (2nd ed.), Addison-Wesley, Reading, ISBN 0-201-01984-1, 1976.
  • [7] Gurel, E., k-Order Gaussian Fibonacci and k-Order Gaussian Lucas Recurrence Relations, Ph.D Thesis, Pamukkale University Institute of Science Mathematics, Denizli, Turkey, 2015.
  • [8] Halici, S., Öz, S., On some Gaussian Pell and Pell-Lucas numbers, Ordu University Science and Technology Journal, 6(1)(2016), 8-18.
  • [9] Halici, S., Öz, S., On Gaussian Pell Polynomials and Their Some Properties, Palestine Journal of Mathematics, 7(1)(2018), 251-256.
  • [10] Harman, C. J., Complex Fibonacci Numbers, Fibonacci Quarterly, 19(1)(1981), 82-86.
  • [11] Horadam, A. F., Complex Fibonacci Numbers and Fibonacci quaternions, American Mathematical Monthly, 70(1963), 289-291.
  • [12] Jordan, J. H., Gaussian Fibonacci and Lucas Numbers, Fibonacci Quarterly, 3(1965), 315-318.
  • [13] Karaaslan, N., Ya˘gmur, T., Gaussian (s,t)-Pell and Pell-Lucas Sequences and Their Matrix Representations, BEU Journal of Science, 8(1)(2019), 46-59.
  • [14] Natividad, L. R., On Solving Fibonacci-Like Sequences of Fourth, Fifth and Sixth Order, International Journal of Mathematics and Computing, 3(2)(2013), 38-40.
  • [15] Pethe S., Horadam A.F., Generalised Gaussian Fibonacci numbers, Bulletin of the Australian Mathematical Society, 33(1986), 37-48.
  • [16] Pethe S., Horadam, A. F., Generalised Gaussian Lucas Primordial numbers, Fibonacci Quarterly, (1988), 20-30. 1988.
  • [17] Pethe, S., Some Identities for Tribonacci Sequences, The Fibonacci Quarterly, 26(1988), 144-151.
  • [18] 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)(2016), 75-80.
  • [19] Simson. R., An Explanation of an Obscure Passage in Albrecht Girard’s Commentary upon Simon Stevin’s Works, Philosophical Transactions of the Royal Society, 48(1)(1753), 368-377.
  • [20] Sloane, N. J. A., The on-line encyclopedia of integer sequences, http://oeis.org/.
  • [21] Soykan, Y., Taşdemir, E., Okumuş, İ., Göcen, M., Gaussian Generalized Tribonacci Numbers, Journal of Progressive Research in Mathematics, 14(2)(2018), 2373-2387.
  • [22] Soykan, Y., Gaussian Generalized Tetranacci Numbers, Journal of Advances in Mathematics and Computer Science, 31(3)(2019), 1-21.
  • [23] Soykan, Y., On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers, Asian Research Journal of Mathematics, 16(9)(2020), 102-121.
  • [24] Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, International Journal of Advances in Applied Mathematics and Mechanics, 7(2)(2019), 45-56.
  • [25] Tas¸cı, D., Acar, H., Gaussian Tetranacci Numbers, Communications in Mathematics ans Applications, 8(3)(2017), 379-386.
  • [26] Tas¸cı, D., Acar, H., Gaussian Padovan and Gaussian Pell-Padovan Numbers, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(2)(2018), 82-88.
  • [27] Yagmur, T., Karaaslan, N., Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence, Aksaray University Journal of Science and Engineering, 2(1)(2018), 63-72.
  • [28] Wolfram, D. A., Solving Generalized Fibonacci Recurrences, Fibonacci Quarterly, (1998), 129-145.

On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers

Year 2021, , 25 - 43, 30.06.2021
https://doi.org/10.47000/tjmcs.787578

Abstract

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Hexanacci numbers, and as special cases, we investigate Hexanacci and Hexanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Hexanacci numbers and as special cases, we investigate Gaussian Hexanacci and Gaussian Hexanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Hexanacci numbers and Gaussian generalized Hexanacci numbers.

References

  • [1] Asci, M., Gurel E., Gaussian Jacobsthal and Gaussian Jacobsthal Polynomials, Notes on Number Theory and Discrete Mathematics, 19(2013), 25-36.
  • [2] Bacani, J. B., Rabago, J. F. T., On Generalized Fibonacci Numbers, Applied Mathematical Sciences,9(25)(2015), 3611-3622.
  • [3] Berzsenyi, G., Gaussian Fibonacci Numbers, Fibonacci Quarterly, 15(3)(1977), 233-236.
  • [4] Catarino, P., Campos, H., A note on Gaussian Modified Pell numbers, Journal of Information & Optimization Sciences, 39(6)(2018), 1363- 1371.
  • [5] Dresden, G. P., Du, Z., A Simplified Binet Formula for k-Generalized Fibonacci Numbers, Journal of Integer Sequences, 17(4)(2014), 1-9.
  • [6] Fraleigh, J. B., A First Course In Abstract Algebra, (2nd ed.), Addison-Wesley, Reading, ISBN 0-201-01984-1, 1976.
  • [7] Gurel, E., k-Order Gaussian Fibonacci and k-Order Gaussian Lucas Recurrence Relations, Ph.D Thesis, Pamukkale University Institute of Science Mathematics, Denizli, Turkey, 2015.
  • [8] Halici, S., Öz, S., On some Gaussian Pell and Pell-Lucas numbers, Ordu University Science and Technology Journal, 6(1)(2016), 8-18.
  • [9] Halici, S., Öz, S., On Gaussian Pell Polynomials and Their Some Properties, Palestine Journal of Mathematics, 7(1)(2018), 251-256.
  • [10] Harman, C. J., Complex Fibonacci Numbers, Fibonacci Quarterly, 19(1)(1981), 82-86.
  • [11] Horadam, A. F., Complex Fibonacci Numbers and Fibonacci quaternions, American Mathematical Monthly, 70(1963), 289-291.
  • [12] Jordan, J. H., Gaussian Fibonacci and Lucas Numbers, Fibonacci Quarterly, 3(1965), 315-318.
  • [13] Karaaslan, N., Ya˘gmur, T., Gaussian (s,t)-Pell and Pell-Lucas Sequences and Their Matrix Representations, BEU Journal of Science, 8(1)(2019), 46-59.
  • [14] Natividad, L. R., On Solving Fibonacci-Like Sequences of Fourth, Fifth and Sixth Order, International Journal of Mathematics and Computing, 3(2)(2013), 38-40.
  • [15] Pethe S., Horadam A.F., Generalised Gaussian Fibonacci numbers, Bulletin of the Australian Mathematical Society, 33(1986), 37-48.
  • [16] Pethe S., Horadam, A. F., Generalised Gaussian Lucas Primordial numbers, Fibonacci Quarterly, (1988), 20-30. 1988.
  • [17] Pethe, S., Some Identities for Tribonacci Sequences, The Fibonacci Quarterly, 26(1988), 144-151.
  • [18] 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)(2016), 75-80.
  • [19] Simson. R., An Explanation of an Obscure Passage in Albrecht Girard’s Commentary upon Simon Stevin’s Works, Philosophical Transactions of the Royal Society, 48(1)(1753), 368-377.
  • [20] Sloane, N. J. A., The on-line encyclopedia of integer sequences, http://oeis.org/.
  • [21] Soykan, Y., Taşdemir, E., Okumuş, İ., Göcen, M., Gaussian Generalized Tribonacci Numbers, Journal of Progressive Research in Mathematics, 14(2)(2018), 2373-2387.
  • [22] Soykan, Y., Gaussian Generalized Tetranacci Numbers, Journal of Advances in Mathematics and Computer Science, 31(3)(2019), 1-21.
  • [23] Soykan, Y., On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers, Asian Research Journal of Mathematics, 16(9)(2020), 102-121.
  • [24] Soykan, Y., Simson Identity of Generalized m-step Fibonacci Numbers, International Journal of Advances in Applied Mathematics and Mechanics, 7(2)(2019), 45-56.
  • [25] Tas¸cı, D., Acar, H., Gaussian Tetranacci Numbers, Communications in Mathematics ans Applications, 8(3)(2017), 379-386.
  • [26] Tas¸cı, D., Acar, H., Gaussian Padovan and Gaussian Pell-Padovan Numbers, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(2)(2018), 82-88.
  • [27] Yagmur, T., Karaaslan, N., Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence, Aksaray University Journal of Science and Engineering, 2(1)(2018), 63-72.
  • [28] Wolfram, D. A., Solving Generalized Fibonacci Recurrences, Fibonacci Quarterly, (1998), 129-145.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Yüksel Soykan 0000-0002-1895-211X

Nejla Özmen 0000-0001-7555-1964

Publication Date June 30, 2021
Published in Issue Year 2021

Cite

APA Soykan, Y., & Özmen, N. (2021). On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers. Turkish Journal of Mathematics and Computer Science, 13(1), 25-43. https://doi.org/10.47000/tjmcs.787578
AMA Soykan Y, Özmen N. On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers. TJMCS. June 2021;13(1):25-43. doi:10.47000/tjmcs.787578
Chicago Soykan, Yüksel, and Nejla Özmen. “On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers”. Turkish Journal of Mathematics and Computer Science 13, no. 1 (June 2021): 25-43. https://doi.org/10.47000/tjmcs.787578.
EndNote Soykan Y, Özmen N (June 1, 2021) On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers. Turkish Journal of Mathematics and Computer Science 13 1 25–43.
IEEE Y. Soykan and N. Özmen, “On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers”, TJMCS, vol. 13, no. 1, pp. 25–43, 2021, doi: 10.47000/tjmcs.787578.
ISNAD Soykan, Yüksel - Özmen, Nejla. “On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers”. Turkish Journal of Mathematics and Computer Science 13/1 (June 2021), 25-43. https://doi.org/10.47000/tjmcs.787578.
JAMA Soykan Y, Özmen N. On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers. TJMCS. 2021;13:25–43.
MLA Soykan, Yüksel and Nejla Özmen. “On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 1, 2021, pp. 25-43, doi:10.47000/tjmcs.787578.
Vancouver Soykan Y, Özmen N. On Generalized Hexanacci and Gaussian Generalized Hexanacci Numbers. TJMCS. 2021;13(1):25-43.