Cite

[1] M. Akyiğit, H.H. Kösal, and M. Tosun, Split Fibonacci quaternions, Adv. Appl. Clifford Algebr. 23 2013, no. 3, 535–545.10.1007/s00006-013-0401-9 Search in Google Scholar

[2] M. Asci and E. Gurel, Gaussian Jacobsthal and Gaussian Jacobsthal Lucas numbers, Ars Combin. 111 2013, 53–63. Search in Google Scholar

[3] G. Berzsenyi, Gaussian Fibonacci numbers, Fibonacci Quart. 15 1977, no. 3, 233–236. Search in Google Scholar

[4] G. Bilgici and P. Catarino, Unrestricted Pell and Pell–Lucas quaternions, Int. J. Math. Syst. Sci. 1 2018, no. 3, Article ID: 816, 4 pp.10.24294/ijmss.v1i3.816 Search in Google Scholar

[5] P. Catarino, The modified Pell and the modified k-Pell quaternions and octonions, Adv. Appl. Clifford Algebr. 26 2016, no. 2, 577–590.10.1007/s00006-015-0611-4 Search in Google Scholar

[6] P. Catarino, Bicomplex k-Pell quaternions, Comput. Methods Funct. Theory 19 (2019), no. 1, 65–76. Search in Google Scholar

[7] P. Catarino, On k-Pell hybrid numbers, J. Discrete Math. Sci. Cryptogr. 22 (2019), no. 1, 83–89. Search in Google Scholar

[8] P. Catarino and A. Borges, A note on incomplete Leonardo numbers, Integers 20 (2020), Paper No. A43, 7 pp. Search in Google Scholar

[9] P. Catarino and A. Borges, On Leonardo numbers, Acta Math. Univ. Comenian. (N.S.) 89 (2020), no. 1, 75–86. Search in Google Scholar

[10] P. Catarino and H. Campos, A note on Gaussian modified Pell numbers, J. Inf. Optim. Sci. 39 (2018), no. 6, 1363–1371. Search in Google Scholar

[11] P. Catarino and P. Vasco, The generalized order-m (k-Pell) numbers, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 66 (2020), no. 1, 55–65. Search in Google Scholar

[12] Y. Choo, A generalized quaternion with generalized Fibonacci number components, Appl. Math. Sci. 14 (2020), no. 1, 31–38. Search in Google Scholar

[13] S. Falcon, On the generating matrices of the k-Fibonacci numbers, Proyecciones 32 (2013), no. 4, 347–357. Search in Google Scholar

[14] S. Halici, On quaternion-Gaussian Lucas numbers, Math. Methods Appl. Sci. 44 (2021), no. 9, 7601–7606. Search in Google Scholar

[15] S. Halici and G. Cerda-Morales, On quaternion-Gaussian Fibonacci numbers and their properties, An. fitiinţ. Univ. “Ovidius” Constanţa Ser. Mat. 29 (2021), no. 1, 71–82. Search in Google Scholar

[16] S. Halici and A. Karataş, On a generalization for Fibonacci quaternions, Chaos Solitons Fractals 98 (2017), 178–182.10.1016/j.chaos.2017.03.037 Search in Google Scholar

[17] S. Halici and S. Öz, On some Gaussian Pell and Pell–Lucas numbers, Ordu Univ. J. Sci. Tech. 6 (2016), no. 1, 8–18. Search in Google Scholar

[18] W.R. Hamilton, Elements of Quaternions, Longmans, Green, & Co., London, 1866. Search in Google Scholar

[19] A.F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Amer. Math. Monthly 70 (1963), 289–291.10.2307/2313129 Search in Google Scholar

[20] L. Huang and W. So, Quadratic formulas for quaternions, Appl. Math. Lett. 15 (2002), no. 5, 533–540. Search in Google Scholar

[21] J.H. Jordan, Gaussian Fibonacci and Lucas numbers, Fibonacci Quart. 3 (1965), 315–318. Search in Google Scholar

[22] M.Y. Kartal, Gaussian Bronze Fibonacci numbers, EJONS Int. J. Math. Eng. Nat. Sci. 4 (2020), no. 13, 19–25. Search in Google Scholar

[23] E. Kılıç and D. Tasci, On the generalized Fibonacci and Pell sequences by Hessenberg matrices, Ars Combin. 94 (2010), 161–174. Search in Google Scholar

[24] E. Kılıç, D. Tasci, and P. Haukkanen, On the generalized Lucas sequences by Hessenberg matrices, Ars Combin. 95 (2010), 383–395. Search in Google Scholar

[25] C. Kızılateş, A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos Solitons Fractals 130 (2020), 109449, 5 pp.10.1016/j.chaos.2019.109449 Search in Google Scholar

[26] T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.10.1002/9781118033067 Search in Google Scholar

[27] C. Levesque, On m-th order linear recurrences, Fibonacci Quart. 23 (1985), no. 4, 290–293. Search in Google Scholar

[28] E. Polatli, C. Kizilates, and S. Kesim, On split k-Fibonacci and k-Lucas quaternions, Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 353–362. Search in Google Scholar

[29] N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences, The OEIS Foundation Inc., http://oeis.org/. Search in Google Scholar

[30] J.L. Synge, Quaternions, Lorentz Transformations, and the Conway-Dirac-Eddington Matrices, Communications of the Dublin Institute for Advanced Studies, Series A, 21, Dublin Inst. for Adv. Stud., Dublin, 1972. Search in Google Scholar

[31] A. Szynal-Liana and I. Włoch, A note on Jacobsthal quaternions, Adv. Appl. Clifford Algebr. 26 (2016), no. 1, 441–447. Search in Google Scholar

[32] D. Tasci, On k-Jacobsthal and k-Jacobsthal–Lucas quaternions, J. Sci. Arts 40 (2017), no. 3, 469–476. Search in Google Scholar

[33] Ü. Tokeşer, Z. Ünal, and G. Bilgici, Split Pell and Pell–Lucas quaternions, Adv. Appl. Clifford Algebr. 27 2017, no. 2, 1881–1893.10.1007/s00006-016-0747-x Search in Google Scholar

[34] T. Yağmur, Split Jacobsthal and Jacobsthal–Lucas quaternions, Commun. Math. Appl. 10 (2019), no. 3, 429–438. Search in Google Scholar

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