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On the Richard and Raoul numbers

Yıl 2022, Cilt: 11 Sayı: 3, 256 - 264, 31.12.2022

Orhan Dışkaya Hamza Menken

https://doi.org/10.54187/jnrs.1201184

Öz

In this study, we define and examine the Richard and Raoul sequences and we deal with, in detail, two special cases, namely, Richard and Raoul sequences. We indicate that there are close relations between Richard and Raoul numbers and Padovan and Perrin numbers. Moreover, we present the Binet-like formulas, generating functions, summation formulas, and some identities for these sequences.

Anahtar Kelimeler

Padovan numbers Perrin numbers Generating functions Binet-like formula Binomial sums

Kaynakça

  • OEIS, The on-line encyclopedia of integer sequences, Retrieved November 15, 2022, https://oeis.org/A000931.
  • T. Koshy, Fibonacci and Lucas numbers with applications, volume 1, John Wiley & Sons, 2018.
  • O. Deveci, E. Karaduman, On the Padovan p-numbers, Hacettepe Journal of Mathematics and Statistics, 46(4), (2017) 579-592.
  • T. Goy, Some families of identities for Padovan numbers, Proceedings of the Jangjeon Mathematical Society, 21(3), (2018) 413-419.
  • S. E. Rihane, C. A. Adegbindin, A. Togbé, Fermat Padovan and Perrin numbers, Journal of Integer Sequences, 23(6), (2020) 1-11.
  • K. Sokhuma, Matrices formula for Padovan and Perrin sequences, Applied Mathematical Sciences, 7(142), (2013) 7093-7096.
  • N. Yılmaz, N. Ta¸skara, Matrix sequences in terms of Padovan and Perrin numbers, Journal of Applied Mathematics, 2013, (2013) Article ID: 941673, 1-7.
  • D. Taşçı, Padovan and Pell-Padovan quaternions, Journal of Science and Arts, 42(1), (2018) 125-132.
  • O. Dişkaya, H. Menken, On the split $(s,t)$-Padovan and $(s,t)$-Perrin quaternions, International Journal of Applied Mathematics and Informatics, 13, (2019) 25-28.
  • O. Dişkaya, H. Menken, Some properties of the plastic constant, Journal of Science and Arts, 21(4), (2021) 883-894.
  • R. P.M. Vieira, F. R. V. Alves, P. M.M. C. Catarino, A historical analysis of the Padovan sequence, International Journal of Trends in Mathematics Education Research, 3(1), (2020) 8-12.
  • OEIS, The on-line encyclopedia of integer sequences, Retrieved November 15, 2022, https://oeis.org/A001608.
  • A. Shannon, P. G. Anderson, A. Horadam, Properties of Cordonnier, Perrin and van der Laan numbers, International Journal of Mathematical Education in Science and Technology, 37(7), (2006) 825–831.
  • Y. Soykan, On generalized Padovan numbers, Preprint, 2021, https://doi.org/10.20944/preprints202110.0101.v1.
  • A. Faisant, On the Padovan sequence, arXiv preprint arXiv:1905.07702„ https://arxiv.org/pdf/1905.07702.pdf.
  • Y. Soykan, Generalized Edouard numbers, International Journal of Advances in Applied Mathematics and Mechanics, 3(9), (2022) 41-52.
  • R. P. Agarwal, S. R. Grace, D. O’Regan, Generalized Ernst numbers, Asian Journal of Pure and Applied Mathematics, 4(3), (2022) 1-15.
  • Y. Soykan, Generalized Oresme numbers, Earthline Journal of Mathematical Sciences, 7(2), (2021) 333-367.
  • Y. Soykan, İ. Okumuş, E. Taşdemir, Generalized Pisano numbers, Notes on Number Theory and Discrete Mathematics, 28(3), (2022) 477-490.
  • Y. Soykan, Generalized John numbers, Journal of Progressive Research in Mathematics, 1(19), (2022) 17-34.
  • Y. Soykan, A study on generalized Jacobsthal-Padovan numbers, Earthline Journal of Mathematical Sciences, 4(2), (2020) 227-251.
  • P. M. Catarino, A. Borges, On Leonardo numbers, Acta Mathematica Universitatis Comenianae, 89(1), (2019) 75-86.
  • OEIS, The on-line encyclopedia of integer sequences, Retrieved November 15, 2022, https://oeis.org/A023434.

Yıl 2022, Cilt: 11 Sayı: 3, 256 - 264, 31.12.2022

Orhan Dışkaya Hamza Menken

https://doi.org/10.54187/jnrs.1201184

Öz

Kaynakça

  • OEIS, The on-line encyclopedia of integer sequences, Retrieved November 15, 2022, https://oeis.org/A000931.
  • T. Koshy, Fibonacci and Lucas numbers with applications, volume 1, John Wiley & Sons, 2018.
  • O. Deveci, E. Karaduman, On the Padovan p-numbers, Hacettepe Journal of Mathematics and Statistics, 46(4), (2017) 579-592.
  • T. Goy, Some families of identities for Padovan numbers, Proceedings of the Jangjeon Mathematical Society, 21(3), (2018) 413-419.
  • S. E. Rihane, C. A. Adegbindin, A. Togbé, Fermat Padovan and Perrin numbers, Journal of Integer Sequences, 23(6), (2020) 1-11.
  • K. Sokhuma, Matrices formula for Padovan and Perrin sequences, Applied Mathematical Sciences, 7(142), (2013) 7093-7096.
  • N. Yılmaz, N. Ta¸skara, Matrix sequences in terms of Padovan and Perrin numbers, Journal of Applied Mathematics, 2013, (2013) Article ID: 941673, 1-7.
  • D. Taşçı, Padovan and Pell-Padovan quaternions, Journal of Science and Arts, 42(1), (2018) 125-132.
  • O. Dişkaya, H. Menken, On the split $(s,t)$-Padovan and $(s,t)$-Perrin quaternions, International Journal of Applied Mathematics and Informatics, 13, (2019) 25-28.
  • O. Dişkaya, H. Menken, Some properties of the plastic constant, Journal of Science and Arts, 21(4), (2021) 883-894.
  • R. P.M. Vieira, F. R. V. Alves, P. M.M. C. Catarino, A historical analysis of the Padovan sequence, International Journal of Trends in Mathematics Education Research, 3(1), (2020) 8-12.
  • OEIS, The on-line encyclopedia of integer sequences, Retrieved November 15, 2022, https://oeis.org/A001608.
  • A. Shannon, P. G. Anderson, A. Horadam, Properties of Cordonnier, Perrin and van der Laan numbers, International Journal of Mathematical Education in Science and Technology, 37(7), (2006) 825–831.
  • Y. Soykan, On generalized Padovan numbers, Preprint, 2021, https://doi.org/10.20944/preprints202110.0101.v1.
  • A. Faisant, On the Padovan sequence, arXiv preprint arXiv:1905.07702„ https://arxiv.org/pdf/1905.07702.pdf.
  • Y. Soykan, Generalized Edouard numbers, International Journal of Advances in Applied Mathematics and Mechanics, 3(9), (2022) 41-52.
  • R. P. Agarwal, S. R. Grace, D. O’Regan, Generalized Ernst numbers, Asian Journal of Pure and Applied Mathematics, 4(3), (2022) 1-15.
  • Y. Soykan, Generalized Oresme numbers, Earthline Journal of Mathematical Sciences, 7(2), (2021) 333-367.
  • Y. Soykan, İ. Okumuş, E. Taşdemir, Generalized Pisano numbers, Notes on Number Theory and Discrete Mathematics, 28(3), (2022) 477-490.
  • Y. Soykan, Generalized John numbers, Journal of Progressive Research in Mathematics, 1(19), (2022) 17-34.
  • Y. Soykan, A study on generalized Jacobsthal-Padovan numbers, Earthline Journal of Mathematical Sciences, 4(2), (2020) 227-251.
  • P. M. Catarino, A. Borges, On Leonardo numbers, Acta Mathematica Universitatis Comenianae, 89(1), (2019) 75-86.
  • OEIS, The on-line encyclopedia of integer sequences, Retrieved November 15, 2022, https://oeis.org/A023434.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Orhan Dışkaya 0000-0001-5698-7834

Hamza Menken 0000-0003-1194-3162

Yayımlanma Tarihi 31 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 11 Sayı: 3

Kaynak Göster

APA Dışkaya, O., & Menken, H. (2022). On the Richard and Raoul numbers. Journal of New Results in Science, 11(3), 256-264. https://doi.org/10.54187/jnrs.1201184
AMA Dışkaya O, Menken H. On the Richard and Raoul numbers. JNRS. Aralık 2022;11(3):256-264. doi:10.54187/jnrs.1201184
Chicago Dışkaya, Orhan, ve Hamza Menken. “On the Richard and Raoul Numbers”. Journal of New Results in Science 11, sy. 3 (Aralık 2022): 256-64. https://doi.org/10.54187/jnrs.1201184.
EndNote Dışkaya O, Menken H (01 Aralık 2022) On the Richard and Raoul numbers. Journal of New Results in Science 11 3 256–264.
IEEE O. Dışkaya ve H. Menken, “On the Richard and Raoul numbers”, JNRS, c. 11, sy. 3, ss. 256–264, 2022, doi: 10.54187/jnrs.1201184.
ISNAD Dışkaya, Orhan - Menken, Hamza. “On the Richard and Raoul Numbers”. Journal of New Results in Science 11/3 (Aralık 2022), 256-264. https://doi.org/10.54187/jnrs.1201184.
JAMA Dışkaya O, Menken H. On the Richard and Raoul numbers. JNRS. 2022;11:256–264.
MLA Dışkaya, Orhan ve Hamza Menken. “On the Richard and Raoul Numbers”. Journal of New Results in Science, c. 11, sy. 3, 2022, ss. 256-64, doi:10.54187/jnrs.1201184.
Vancouver Dışkaya O, Menken H. On the Richard and Raoul numbers. JNRS. 2022;11(3):256-64.
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