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Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions

Yıl 2023, Cilt: 6 Sayı: 2, 98 - 101, 01.04.2023

Zafer Ünal

https://doi.org/10.34248/bsengineering.1253548

Öz

Fibonacci and Lucas numbers have been the most popular integer sequences since they were defined. These integer sequences have many uses, from nature to computer science, from art to financial analysis. Many researchers have worked on this subject. Sedenions form a 16-dimensional algebra on the field of real numbers. Various systems can be constructed by using the terms of special integer sequences instead of terms in sedenions. In this study, we define dual Fibonacci (DFS) and dual Lucas sedenions (DLS) with the help of Fibonacci and Lucas termed sedenions. Then we calculate some special identities for DFS and DLS such as Vajda's, Catalan's, d'Ocagne's, Cassini's.

Anahtar Kelimeler

Fibonacci and Lucas numbers Dual numbers Sedenions Vajda’s identity Binet-like formula

Kaynakça

  • Bilgici G. 2014. New generalizations of Fibonacci and Lucas sequences. Appl Math Sci, 8(29): 1429-1437.
  • Bilgici G, Tokeşer Ü, Ünal Z. 2017. Fibonacci and Lucas Sedenions. J Integer Seq, 20: 17.1.8.
  • Cawagas RE. 2004. On the structure and zero divisors of the Cayley-Dickson sedenion algebra. Discuss Math Gen Algebra Appl, 24: 251-265.
  • Clifford WK. 1871. Preliminary sketch of bi-quaternions. Proc Lond Math Soc, 4(1): 381-395.
  • Horadam AF. 1961. A generalized Fibonacci sequence. The American Math Monthly, 68(5): 455-459.
  • Imaeda K, Imaeda M, 2000. Sedenions: algebra and analysis. Appl Math Comput, 115: 77-88.
  • Koshy T. 2001. Fibonacci and lucas numbers with applications. Wiley-Interscience Publication, Quebec, Canada, pp: 77-78.
  • Muskat JB. 1993. Generalized Fibonacci and Lucas sequences and rootfinding methods. Math Comput, 61(203): 365-372.
  • Tokeşer Ü, Mert T, Dündar Y. 2022. Some properties and Vajda theorems of split dual Fibonacci and split dual Lucas octonions. AIMS Math, 7(5): 8645-8653.
  • Ünal Z, Tokeşer Ü, Bilgici G. 2017. Some properties of dual Fibonacci and dual Lucas octonions. Adv Appl Clifford Algebras, 27: 1907-1916.
  • Wilcox HJ. 1986. Fibonacci sequences of period n in groups. Fibonacci Quart, 24(4): 356-361.
  • Yayenie O. 2011. A note on generalized Fibonacci sequences. Appl Math Comput, 217(12): 5603-5611.

Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions

Yıl 2023, Cilt: 6 Sayı: 2, 98 - 101, 01.04.2023

Zafer Ünal

https://doi.org/10.34248/bsengineering.1253548

Öz

Fibonacci and Lucas numbers have been the most popular integer sequences since they were defined. These integer sequences have many uses, from nature to computer science, from art to financial analysis. Many researchers have worked on this subject. Sedenions form a 16-dimensional algebra on the field of real numbers. Various systems can be constructed by using the terms of special integer sequences instead of terms in sedenions. In this study, we define dual Fibonacci (DFS) and dual Lucas sedenions (DLS) with the help of Fibonacci and Lucas termed sedenions. Then we calculate some special identities for DFS and DLS such as Vajda's, Catalan's, d'Ocagne's, Cassini's.

Anahtar Kelimeler

Fibonacci and Lucas numbers Dual numbers Sedenions Vajda’s identity Binet-like formula

Kaynakça

  • Bilgici G. 2014. New generalizations of Fibonacci and Lucas sequences. Appl Math Sci, 8(29): 1429-1437.
  • Bilgici G, Tokeşer Ü, Ünal Z. 2017. Fibonacci and Lucas Sedenions. J Integer Seq, 20: 17.1.8.
  • Cawagas RE. 2004. On the structure and zero divisors of the Cayley-Dickson sedenion algebra. Discuss Math Gen Algebra Appl, 24: 251-265.
  • Clifford WK. 1871. Preliminary sketch of bi-quaternions. Proc Lond Math Soc, 4(1): 381-395.
  • Horadam AF. 1961. A generalized Fibonacci sequence. The American Math Monthly, 68(5): 455-459.
  • Imaeda K, Imaeda M, 2000. Sedenions: algebra and analysis. Appl Math Comput, 115: 77-88.
  • Koshy T. 2001. Fibonacci and lucas numbers with applications. Wiley-Interscience Publication, Quebec, Canada, pp: 77-78.
  • Muskat JB. 1993. Generalized Fibonacci and Lucas sequences and rootfinding methods. Math Comput, 61(203): 365-372.
  • Tokeşer Ü, Mert T, Dündar Y. 2022. Some properties and Vajda theorems of split dual Fibonacci and split dual Lucas octonions. AIMS Math, 7(5): 8645-8653.
  • Ünal Z, Tokeşer Ü, Bilgici G. 2017. Some properties of dual Fibonacci and dual Lucas octonions. Adv Appl Clifford Algebras, 27: 1907-1916.
  • Wilcox HJ. 1986. Fibonacci sequences of period n in groups. Fibonacci Quart, 24(4): 356-361.
  • Yayenie O. 2011. A note on generalized Fibonacci sequences. Appl Math Comput, 217(12): 5603-5611.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Research Articles
Yazarlar

Zafer Ünal 0000-0003-2445-1028

Yayımlanma Tarihi 1 Nisan 2023
Gönderilme Tarihi 20 Şubat 2023
Kabul Tarihi 11 Mart 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 2

Kaynak Göster

APA Ünal, Z. (2023). Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions. Black Sea Journal of Engineering and Science, 6(2), 98-101. https://doi.org/10.34248/bsengineering.1253548
AMA Ünal Z. Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions. BSJ Eng. Sci. Nisan 2023;6(2):98-101. doi:10.34248/bsengineering.1253548
Chicago Ünal, Zafer. “Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions”. Black Sea Journal of Engineering and Science 6, sy. 2 (Nisan 2023): 98-101. https://doi.org/10.34248/bsengineering.1253548.
EndNote Ünal Z (01 Nisan 2023) Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions. Black Sea Journal of Engineering and Science 6 2 98–101.
IEEE Z. Ünal, “Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions”, BSJ Eng. Sci., c. 6, sy. 2, ss. 98–101, 2023, doi: 10.34248/bsengineering.1253548.
ISNAD Ünal, Zafer. “Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions”. Black Sea Journal of Engineering and Science 6/2 (Nisan 2023), 98-101. https://doi.org/10.34248/bsengineering.1253548.
JAMA Ünal Z. Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions. BSJ Eng. Sci. 2023;6:98–101.
MLA Ünal, Zafer. “Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions”. Black Sea Journal of Engineering and Science, c. 6, sy. 2, 2023, ss. 98-101, doi:10.34248/bsengineering.1253548.
Vancouver Ünal Z. Vajda’s Identities for Dual Fibonacci and Dual Lucas Sedenions. BSJ Eng. Sci. 2023;6(2):98-101.
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