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On the Richard and Raoul numbers

Year 2022, Volume: 11 Issue: 3, 256 - 264, 31.12.2022
https://doi.org/10.54187/jnrs.1201184

Abstract

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.

References

  • 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.
Year 2022, Volume: 11 Issue: 3, 256 - 264, 31.12.2022
https://doi.org/10.54187/jnrs.1201184

Abstract

References

  • 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.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Orhan Dışkaya 0000-0001-5698-7834

Hamza Menken 0000-0003-1194-3162

Publication Date December 31, 2022
Published in Issue Year 2022 Volume: 11 Issue: 3

Cite

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. December 2022;11(3):256-264. doi:10.54187/jnrs.1201184
Chicago Dışkaya, Orhan, and Hamza Menken. “On the Richard and Raoul Numbers”. Journal of New Results in Science 11, no. 3 (December 2022): 256-64. https://doi.org/10.54187/jnrs.1201184.
EndNote Dışkaya O, Menken H (December 1, 2022) On the Richard and Raoul numbers. Journal of New Results in Science 11 3 256–264.
IEEE O. Dışkaya and H. Menken, “On the Richard and Raoul numbers”, JNRS, vol. 11, no. 3, pp. 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 (December 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 and Hamza Menken. “On the Richard and Raoul Numbers”. Journal of New Results in Science, vol. 11, no. 3, 2022, pp. 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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