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The Representation and Finite Sums of the Padovan-p Jacobsthal Numbers

Yıl 2021, Cilt: 6 Sayı: 3, 134 - 141, 30.12.2021

Öz

In this paper, we consider the Padovan-p Jacobsthal sequence and then we discuss the connection of the Padovan-p Jacobsthal numbers and Jacobsthal numbers. Furthermore, we give the permanental, determinantal, combinatorial, and exponential representations, and the sums of the Padovan-p Jacobsthal numbers by the aid of the generating function and generating matrix of this sequence.

Kaynakça

  • Akuzum Y. The Hadamard-type Padovan-p Sequences, Turkish Journal of Science. 5(2), 2020, 102−109.
  • Akuzum Y. The Padovan-p Jacobsthal Numbers and Binet Formulas. 3. International Baku Scientific Research Congress. 15-16 October 2021, Baku Eurasıa University, Baku, Azerbaijan.
  • Akuzum Y, Deveci O, Shannon AG. On the Pell p-circulant Sequences. Notes on Number Theory and Discrete Mathematics. 23(2), 2017, 91−103.
  • Akuzum Y, Deveci O. The Arrowhead-Jacobsthal Sequences. Mathematica Montisnigri. Vol-LI, 2021, 31−44.
  • Bradie B. Extension and refinements of some properties of sums involving Pell number. Missouri Journal of Mathematical Sciences. 22(1), 2010, 37−43.
  • Brualdi RA, Gibson PM. Convex polyhedra of doubly stochastic matrices I: applications of permanent function. Journal of Combinatorial Theory, Series A. 22(2), 1977, 194−230.
  • Chen WYC, Louck JD. The combinatorial power of the companion matrix. Linear Algebra and its Applications. 232, 1996, 261−278.
  • Deveci O. On the connections among Fibonacci, Pell, Jacobsthal and Padovan numbers. Notes on Number Theory and Discrete Mathematics. 27(2), 2021, 111−128.
  • Deveci O, Karaduman E. On the Padovan p-numbers. Hacettepe Journal of Mathematics and Statistics. 46(4), 2017, 579−592.
  • Deveci O, Adiguzel Z, Akuzum Y. On the Jacobsthal-circulant-Hurwitz Numbers. Maejo International Journal of Science and Technology. 14(1), 2020, 56−67.
  • Erdag O, Deveci O. On The Connections Between Padovan Numbers and Padovan p-Numbers. International Journal of Open Problems in Computer Science and Mathematics. 13(4), 2020, 33−47.
  • Horadam A. Jacobsthal representations numbers. Fibonacci Quarterly. 34(1), 1996, 40−54.
  • Horadam A. Applications of modified Pell numbers to representations. Ulam Quarterly. 3(1), 1994, 34−53.
  • Kalman D. Generalized Fibonacci numbers by matrix methods. Fibonacci Quarterly. 20(1), 1982, 73−76.
  • Kilic E. The Binet formula, sums and representations of generalized Fibonacci p-numbers. European Journal of Combinatorics. 29(3), 2008, 701−711.
  • Kilic E. The generalized Pell (p, i)-numbers and their Binet formulas, combinatorial representations, sums. Chaos, Solitons and Fractals. 40(4), 2009, 2047−2063.
  • Kilic E, Tasci D. The generalized Binet formula, representation and sums of the generalized order-k Pell numbers. Taiwanese Journal of Mathematics. 10(6), 2006, 1661−1670.
  • Koken F, Bozkurt D. On the Jacobsthal numbers by matrix methods. International Journal of Contemporary Mathematical Sciences. 3(13), 2008, 605−614.
  • Lancaster P, Tismenetsky M. The theory of matrices: with applications. Elsevier. 1985.
  • Lidl R, Niederreiter H. Introduction to finite fields and their applications. Cambridge UP. 1986.
  • Shannon AG, Erdag O, Deveci O. On the Connections Between Pell Numbers and Fibonacci p-Numbers. Notes on Number Theory and Discrete Mathematics. 27(1), 2021, 148−160.
Yıl 2021, Cilt: 6 Sayı: 3, 134 - 141, 30.12.2021

Öz

Kaynakça

  • Akuzum Y. The Hadamard-type Padovan-p Sequences, Turkish Journal of Science. 5(2), 2020, 102−109.
  • Akuzum Y. The Padovan-p Jacobsthal Numbers and Binet Formulas. 3. International Baku Scientific Research Congress. 15-16 October 2021, Baku Eurasıa University, Baku, Azerbaijan.
  • Akuzum Y, Deveci O, Shannon AG. On the Pell p-circulant Sequences. Notes on Number Theory and Discrete Mathematics. 23(2), 2017, 91−103.
  • Akuzum Y, Deveci O. The Arrowhead-Jacobsthal Sequences. Mathematica Montisnigri. Vol-LI, 2021, 31−44.
  • Bradie B. Extension and refinements of some properties of sums involving Pell number. Missouri Journal of Mathematical Sciences. 22(1), 2010, 37−43.
  • Brualdi RA, Gibson PM. Convex polyhedra of doubly stochastic matrices I: applications of permanent function. Journal of Combinatorial Theory, Series A. 22(2), 1977, 194−230.
  • Chen WYC, Louck JD. The combinatorial power of the companion matrix. Linear Algebra and its Applications. 232, 1996, 261−278.
  • Deveci O. On the connections among Fibonacci, Pell, Jacobsthal and Padovan numbers. Notes on Number Theory and Discrete Mathematics. 27(2), 2021, 111−128.
  • Deveci O, Karaduman E. On the Padovan p-numbers. Hacettepe Journal of Mathematics and Statistics. 46(4), 2017, 579−592.
  • Deveci O, Adiguzel Z, Akuzum Y. On the Jacobsthal-circulant-Hurwitz Numbers. Maejo International Journal of Science and Technology. 14(1), 2020, 56−67.
  • Erdag O, Deveci O. On The Connections Between Padovan Numbers and Padovan p-Numbers. International Journal of Open Problems in Computer Science and Mathematics. 13(4), 2020, 33−47.
  • Horadam A. Jacobsthal representations numbers. Fibonacci Quarterly. 34(1), 1996, 40−54.
  • Horadam A. Applications of modified Pell numbers to representations. Ulam Quarterly. 3(1), 1994, 34−53.
  • Kalman D. Generalized Fibonacci numbers by matrix methods. Fibonacci Quarterly. 20(1), 1982, 73−76.
  • Kilic E. The Binet formula, sums and representations of generalized Fibonacci p-numbers. European Journal of Combinatorics. 29(3), 2008, 701−711.
  • Kilic E. The generalized Pell (p, i)-numbers and their Binet formulas, combinatorial representations, sums. Chaos, Solitons and Fractals. 40(4), 2009, 2047−2063.
  • Kilic E, Tasci D. The generalized Binet formula, representation and sums of the generalized order-k Pell numbers. Taiwanese Journal of Mathematics. 10(6), 2006, 1661−1670.
  • Koken F, Bozkurt D. On the Jacobsthal numbers by matrix methods. International Journal of Contemporary Mathematical Sciences. 3(13), 2008, 605−614.
  • Lancaster P, Tismenetsky M. The theory of matrices: with applications. Elsevier. 1985.
  • Lidl R, Niederreiter H. Introduction to finite fields and their applications. Cambridge UP. 1986.
  • Shannon AG, Erdag O, Deveci O. On the Connections Between Pell Numbers and Fibonacci p-Numbers. Notes on Number Theory and Discrete Mathematics. 27(1), 2021, 148−160.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume VI Issue III
Yazarlar

Özgür Erdağ 0000-0001-8071-6794

Ömür Deveci 0000-0001-5870-5298

Yayımlanma Tarihi 30 Aralık 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 6 Sayı: 3

Kaynak Göster

APA Erdağ, Ö., & Deveci, Ö. (2021). The Representation and Finite Sums of the Padovan-p Jacobsthal Numbers. Turkish Journal of Science, 6(3), 134-141.
AMA Erdağ Ö, Deveci Ö. The Representation and Finite Sums of the Padovan-p Jacobsthal Numbers. TJOS. Aralık 2021;6(3):134-141.
Chicago Erdağ, Özgür, ve Ömür Deveci. “The Representation and Finite Sums of the Padovan-P Jacobsthal Numbers”. Turkish Journal of Science 6, sy. 3 (Aralık 2021): 134-41.
EndNote Erdağ Ö, Deveci Ö (01 Aralık 2021) The Representation and Finite Sums of the Padovan-p Jacobsthal Numbers. Turkish Journal of Science 6 3 134–141.
IEEE Ö. Erdağ ve Ö. Deveci, “The Representation and Finite Sums of the Padovan-p Jacobsthal Numbers”, TJOS, c. 6, sy. 3, ss. 134–141, 2021.
ISNAD Erdağ, Özgür - Deveci, Ömür. “The Representation and Finite Sums of the Padovan-P Jacobsthal Numbers”. Turkish Journal of Science 6/3 (Aralık 2021), 134-141.
JAMA Erdağ Ö, Deveci Ö. The Representation and Finite Sums of the Padovan-p Jacobsthal Numbers. TJOS. 2021;6:134–141.
MLA Erdağ, Özgür ve Ömür Deveci. “The Representation and Finite Sums of the Padovan-P Jacobsthal Numbers”. Turkish Journal of Science, c. 6, sy. 3, 2021, ss. 134-41.
Vancouver Erdağ Ö, Deveci Ö. The Representation and Finite Sums of the Padovan-p Jacobsthal Numbers. TJOS. 2021;6(3):134-41.