Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 25 Sayı: 4, 969 - 973, 30.08.2021
https://doi.org/10.16984/saufenbilder.842489

Öz

Kaynakça

  • Barry, P. 2005. ‘’A Catalan transform and related transformations on integer sequences’’. J.Integer Seq., 8(4), 1-24.
  • Horadam, A. F. 1961. ‘’A generalized Fibonacci sequence’’. Amer. Math. Monthly, 68 (5), 455–459.
  • Falcon, S. (2013). ‘’Catalan Transform of the k-Fibonacci sequence’’. Commun. Korean Math. Soc. 28(4), 827–832.
  • Koshy, T. 2001. ‘’Fibonacci and Lucas Numbers with Applications’’. New York, NY: Wiley-Interscience Publication.
  • Falc´on, S., and Plaza, A. 2007. ‘’On the Fibonacci k-numbers’’, Chaos Solitons Fractals 32(5), 1615–1624.
  • Layman, J. W. 2001. ‘’The Hankel transform and some of its properties’’. J. Integer Seq. 4(1), 1-11.
  • Bruhn, H. Gellert, L. Günther, J. 2015.‘’Jacobsthal numbers in generalized Petersen graphs’’ Electronic Notes in Discrete Mathematics, 49, 465-472.
  • Anuradha, N. 2008. ‘’Number of points on certain hyperelliptic curves defined over finite fields’’ Finite Fields and Their Applications, 14, 314-328.
  • Sloane, N. J. A., 2007. The on-line encyclopedia of integer sequences, www.research.att.com/˜njas/sequences/
  • http://en.wikipedia.org/wiki/Catalan number
  • Boussayoud, A., Kerada, M. and , Harrouche, N. 2017. ‘’On the k -Lucas Numbers and Lucas Polynomials’’, Turkish Journal of Analysis and Number Theory, 5(4), 121-125.
  • Özkan E., Altun İ., Göçer A. 2017, "On Relationship Among A New Family of k-Fibonacci, k-Lucas Numbers, Fibonacci And Lucas Numbers", Chiang Mai Journal of Scıence, 44, 1744-1750.
  • Taştan, M.,Özkan, E. 2020. ‘’Catalan Transform of The k−Jacobsthal Sequence’’, Electronic Journal of Mathematical Analysis and Applications, 8(2), 70-74.
  • Özkan, E., Taştan, M., Aydoğdu, A. 2019. ‘’3-Fibonacci Polynomials in The Family of Fibonacci Numbers’’, Erzincan University Journal of the Institute of Science and Technology, 12(2), 926-933.
  • Rajkovi´c, P. M., Petkovi´c, M. D. and Barry, P. 2007. ‘’The Hankel transform of the sum of consecutive generalized Catalan numbers. Integral Transforms Spec. Funct’’. 18(4), 285–296.

A New Approach to k-Jacobsthal Lucas Sequences

Yıl 2021, Cilt: 25 Sayı: 4, 969 - 973, 30.08.2021
https://doi.org/10.16984/saufenbilder.842489

Öz

In this study, 〖CS〗_(k,n) of S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas sequences is defined. S_(k,n) Catalan transformation of 𝑘−Jacobsthal-Lucas S_(k,n) sequences is obtained.In addition the transformation of CS_(k,n) is written as the product of the Catalan matrix C, which is the lower triangular matrix, and the S_k matrix of type 𝑛 𝑥 1, and the Hankel transformations of some k-Jacobsthal-Lucas numbers has been found.

Kaynakça

  • Barry, P. 2005. ‘’A Catalan transform and related transformations on integer sequences’’. J.Integer Seq., 8(4), 1-24.
  • Horadam, A. F. 1961. ‘’A generalized Fibonacci sequence’’. Amer. Math. Monthly, 68 (5), 455–459.
  • Falcon, S. (2013). ‘’Catalan Transform of the k-Fibonacci sequence’’. Commun. Korean Math. Soc. 28(4), 827–832.
  • Koshy, T. 2001. ‘’Fibonacci and Lucas Numbers with Applications’’. New York, NY: Wiley-Interscience Publication.
  • Falc´on, S., and Plaza, A. 2007. ‘’On the Fibonacci k-numbers’’, Chaos Solitons Fractals 32(5), 1615–1624.
  • Layman, J. W. 2001. ‘’The Hankel transform and some of its properties’’. J. Integer Seq. 4(1), 1-11.
  • Bruhn, H. Gellert, L. Günther, J. 2015.‘’Jacobsthal numbers in generalized Petersen graphs’’ Electronic Notes in Discrete Mathematics, 49, 465-472.
  • Anuradha, N. 2008. ‘’Number of points on certain hyperelliptic curves defined over finite fields’’ Finite Fields and Their Applications, 14, 314-328.
  • Sloane, N. J. A., 2007. The on-line encyclopedia of integer sequences, www.research.att.com/˜njas/sequences/
  • http://en.wikipedia.org/wiki/Catalan number
  • Boussayoud, A., Kerada, M. and , Harrouche, N. 2017. ‘’On the k -Lucas Numbers and Lucas Polynomials’’, Turkish Journal of Analysis and Number Theory, 5(4), 121-125.
  • Özkan E., Altun İ., Göçer A. 2017, "On Relationship Among A New Family of k-Fibonacci, k-Lucas Numbers, Fibonacci And Lucas Numbers", Chiang Mai Journal of Scıence, 44, 1744-1750.
  • Taştan, M.,Özkan, E. 2020. ‘’Catalan Transform of The k−Jacobsthal Sequence’’, Electronic Journal of Mathematical Analysis and Applications, 8(2), 70-74.
  • Özkan, E., Taştan, M., Aydoğdu, A. 2019. ‘’3-Fibonacci Polynomials in The Family of Fibonacci Numbers’’, Erzincan University Journal of the Institute of Science and Technology, 12(2), 926-933.
  • Rajkovi´c, P. M., Petkovi´c, M. D. and Barry, P. 2007. ‘’The Hankel transform of the sum of consecutive generalized Catalan numbers. Integral Transforms Spec. Funct’’. 18(4), 285–296.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Hakan Akkuş 0000-0001-9716-9424

Rabia Nagehan Üregen 0000-0002-6824-4752

Engin Özkan 0000-0002-4188-7248

Yayımlanma Tarihi 30 Ağustos 2021
Gönderilme Tarihi 1 Mart 2021
Kabul Tarihi 24 Haziran 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 25 Sayı: 4

Kaynak Göster

APA Akkuş, H., Üregen, R. N., & Özkan, E. (2021). A New Approach to k-Jacobsthal Lucas Sequences. Sakarya University Journal of Science, 25(4), 969-973. https://doi.org/10.16984/saufenbilder.842489
AMA Akkuş H, Üregen RN, Özkan E. A New Approach to k-Jacobsthal Lucas Sequences. SAUJS. Ağustos 2021;25(4):969-973. doi:10.16984/saufenbilder.842489
Chicago Akkuş, Hakan, Rabia Nagehan Üregen, ve Engin Özkan. “A New Approach to K-Jacobsthal Lucas Sequences”. Sakarya University Journal of Science 25, sy. 4 (Ağustos 2021): 969-73. https://doi.org/10.16984/saufenbilder.842489.
EndNote Akkuş H, Üregen RN, Özkan E (01 Ağustos 2021) A New Approach to k-Jacobsthal Lucas Sequences. Sakarya University Journal of Science 25 4 969–973.
IEEE H. Akkuş, R. N. Üregen, ve E. Özkan, “A New Approach to k-Jacobsthal Lucas Sequences”, SAUJS, c. 25, sy. 4, ss. 969–973, 2021, doi: 10.16984/saufenbilder.842489.
ISNAD Akkuş, Hakan vd. “A New Approach to K-Jacobsthal Lucas Sequences”. Sakarya University Journal of Science 25/4 (Ağustos 2021), 969-973. https://doi.org/10.16984/saufenbilder.842489.
JAMA Akkuş H, Üregen RN, Özkan E. A New Approach to k-Jacobsthal Lucas Sequences. SAUJS. 2021;25:969–973.
MLA Akkuş, Hakan vd. “A New Approach to K-Jacobsthal Lucas Sequences”. Sakarya University Journal of Science, c. 25, sy. 4, 2021, ss. 969-73, doi:10.16984/saufenbilder.842489.
Vancouver Akkuş H, Üregen RN, Özkan E. A New Approach to k-Jacobsthal Lucas Sequences. SAUJS. 2021;25(4):969-73.

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