The Hyperbolic Quadrapell Sequences

Year 2021, Volume: 7 Issue: 1, 25 - 29, 30.05.2021

Sait Taş

Abstract

In this paper, we extend Quadrapell numbers to Hyperbolic Quadarapell numbers, respectively. Moreover we obtain Binet-like formulas, generating functions and some identities related with Hyperbolic Quadarpell numbers.

Keywords

pell numbers, Quadrapell numbers, hyperbolic numbers, hyperbolic quadrapell numbers

References

• ATANASSOV, K., DIMITROV, D., SHANNON, A.(2009). A remark on ψ-function and pell-padovan's sequence, Notes on Number Theory and Discrete Mathematics, 15(2), 1-44.
• AYDIN, F.T.(2019). Hyperbolic Fibonacci sequence, Universal Journal of Mathematics and Applications, 2(2), 59-64.
• BARREİRA, L., POPESCU, L.H., VALLS, C.(2016). Hyperbolic sequences of linear operators and evolution maps, Milan Journal of Mathematics, 84(2), 203-216.
• BERZSENYİ, G.(1977). Gaussian fibonacci numbers
• CATONİ, F., BOCCALETTİ, D., CANNATA, R., CATONİ, V., NİCHELATTİ, E., ZAMPETTİ, P. (2008). The mathematics of Minkowski space-time: with an introduction to commutative hypercomplex numbers, Springer Science & Business Media.
• ÇAĞMAN, A. Repdigits as Product of Fibonacci and Pell numbers. Turkish Journal of Science, 6(1), 31-35.
• ÇAĞMAN, A. Explicit Solutions of Powers of Three as Sums of Three Pell Numbers Based on Baker’s Type Inequalities. Turkish Journal of Inequalities, 5(1), 93-103.
• ÇAĞMAN, A., and POLAT, K., 2021. On a Diophantine equation related to the difference of two Pell numbers. Contributions to Mathematics. Volume 3, 37-42.
• DEVECİ, Ö., KARADUMAN, E.(2015). The pell sequences in finite groups. Util. Math, 96, 263-276.
• DEVECİ, Ö., SHANNON, A.G.(2018). The quaternion-pell sequence. Communication in Algebra, 46(12), 50403-5409.
• DEVECİ, Ö., SHANNON, A.G.(2020). The complex-type k- Fibonacci sequences and their applications. Communication in Algebra, pages 1-16.
• GARGOUBI, H., KOSSENTINI, S. (2016). f-algebra structure on hyperbolic numbers, Advances in Applied Clifford Algebras, 26(4), 1211-1233.
• GÜNCAN, A., ERBIL, Y. (2012). The q-fibonacci hyperbolic functions, In AIP Conference Proceedings, American Institute of Physics, volume 1479, pages 946-949.
• HORADAM, A.F. (1963). Complex fibonacci numbers and fibonacci quaternions, The American Mathematical Monthly, 70(3), 289-291.
• KHADJIEV, D., GÖKSAL, Y. (2016). Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-euclidean space, Advances in Applied Clifford Algebras, 26(2), 645-668.
• MOTTER, A.E., ROSA, M.A.F. (2016). Hyperbolic calculus, Advances in Applied Clifford Algebras, 8(1), 109-128.
• SHANNON, A.G., HORADAM, A.F., ANDERSON, P.G. (2006). The auxiliary equation associated with the plastic number, Notes on Number Theory and Discrete Mathematics, 12(1), 1-12.
• SHANNON, A.G., ANDERSON, P.G., HORADAM, A.F. (2006). Properties of cordonnier, perrin and van der laan numbers, International Journal of Mathematical Education in Science and Technology, 37(7), 825-831.
• TAS, S., DEVECI, O., KARADUMAN, E. (2014). The fibonacci-padovan sequences in fnite groups, Maejo International Journal of Science And Technology, 8(3), 279-287.
• TAŞCI, D. (2018). Gaussian padovan and gaussian pell-padovan sequences, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(2), 82-88.
• VOET, C. (2012). The poetics of order: Dom hans van der laan's architectonic space, Architectural Research Quarterly, 16(2), 137.