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SOME IDENTITIES FOR GENERALIZED FIBONACCI AND LUCAS SEQUENCES
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.
Keywords
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
Details
Primary Language
English
Subjects
Statistics
Journal Section
Research Article
Publication Date
April 1, 2013
Submission Date
May 11, 2014
Acceptance Date
-
Published in Issue
Year 2013 Volume: 42 Number: 4
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