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SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES

Year 2013, Volume: 42 Issue: 4 , 331 - 338 , 01.04.2013
https://izlik.org/JA57NY94UW

Abstract

In this study, we define a generalization of Lucas sequence{p n }. Thenwe obtain Binet formula of sequence{p n } . Also, we investigate relationships between generalized Fibonacci and Lucas sequences.

References

  • Horadam, A. F. A generalized Fibonacci Sequence, Amer. Math. Monthly, 68, 455–459, 1961. Edson, M. and Yayenie, O. A new generalization of Fibonacci sequences and extended Binet’s Formula, Integer 9, (#A48), 639–654, 2009.
  • Yayenie, O. A note on generalized Fibonacci sequences, Applied. Math. Comp. 217 (12), 5603–5611, 2011.
  • Koshy, T. Fibonacci And Lucas Numbers with Applications, Wiley, New York, 2001.
  • Vajda, S. Fibonacci & Lucas Numbers and the Golden Section, Theory and Applications, Ellis Horwood Ltd., Chishester, 1989.
  • Cooper, C. An identity for period k second order linear recurrence systems, Cong. Numer. 200, 95–106, 2010.
  • Sahin, M. The Gelin-Cesaro identity in some conditional Sequences, Hacettepe Journal of Mathematics and Statistics, 40, 855–861, 2011.
  • Irmak, N. and Szalay, L. On k −periodic Binary Recurrence, Ann. Math. Inform. 40, 25–35, 20

SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES

Year 2013, Volume: 42 Issue: 4 , 331 - 338 , 01.04.2013
https://izlik.org/JA57NY94UW

Abstract

References

  • Horadam, A. F. A generalized Fibonacci Sequence, Amer. Math. Monthly, 68, 455–459, 1961. Edson, M. and Yayenie, O. A new generalization of Fibonacci sequences and extended Binet’s Formula, Integer 9, (#A48), 639–654, 2009.
  • Yayenie, O. A note on generalized Fibonacci sequences, Applied. Math. Comp. 217 (12), 5603–5611, 2011.
  • Koshy, T. Fibonacci And Lucas Numbers with Applications, Wiley, New York, 2001.
  • Vajda, S. Fibonacci & Lucas Numbers and the Golden Section, Theory and Applications, Ellis Horwood Ltd., Chishester, 1989.
  • Cooper, C. An identity for period k second order linear recurrence systems, Cong. Numer. 200, 95–106, 2010.
  • Sahin, M. The Gelin-Cesaro identity in some conditional Sequences, Hacettepe Journal of Mathematics and Statistics, 40, 855–861, 2011.
  • Irmak, N. and Szalay, L. On k −periodic Binary Recurrence, Ann. Math. Inform. 40, 25–35, 20
There are 7 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Research Article
Authors

Nurettin Irmak This is me

Murat Alp This is me

Publication Date April 1, 2013
IZ https://izlik.org/JA57NY94UW
Published in Issue Year 2013 Volume: 42 Issue: 4

Cite

APA Irmak, N., & Alp, M. (2013). SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Hacettepe Journal of Mathematics and Statistics, 42(4), 331-338. https://izlik.org/JA57NY94UW
AMA 1.Irmak N, Alp M. SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Hacettepe Journal of Mathematics and Statistics. 2013;42(4):331-338. https://izlik.org/JA57NY94UW
Chicago Irmak, Nurettin, and Murat Alp. 2013. “SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES”. Hacettepe Journal of Mathematics and Statistics 42 (4): 331-38. https://izlik.org/JA57NY94UW.
EndNote Irmak N, Alp M (April 1, 2013) SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Hacettepe Journal of Mathematics and Statistics 42 4 331–338.
IEEE [1]N. Irmak and M. Alp, “SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 4, pp. 331–338, Apr. 2013, [Online]. Available: https://izlik.org/JA57NY94UW
ISNAD Irmak, Nurettin - Alp, Murat. “SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES”. Hacettepe Journal of Mathematics and Statistics 42/4 (April 1, 2013): 331-338. https://izlik.org/JA57NY94UW.
JAMA 1.Irmak N, Alp M. SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Hacettepe Journal of Mathematics and Statistics. 2013;42:331–338.
MLA Irmak, Nurettin, and Murat Alp. “SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 4, Apr. 2013, pp. 331-8, https://izlik.org/JA57NY94UW.
Vancouver 1.Nurettin Irmak, Murat Alp. SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Hacettepe Journal of Mathematics and Statistics [Internet]. 2013 Apr. 1;42(4):331-8. Available from: https://izlik.org/JA57NY94UW