Relevant bibliographies by topics / Fibonacci numbers

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Academic literature on the topic 'Fibonacci numbers'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Fibonacci numbers"

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KÖKEN, Fikri, and Emre KANKAL. "Altered Numbers of Fibonacci Number Squared." Journal of New Theory, no. 45 (December 31, 2023): 73–82. http://dx.doi.org/10.53570/jnt.1368751.

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We investigate two types of altered Fibonacci numbers obtained by adding or subtracting a specific value $\{a\}$ from the square of the $n^{th}$ Fibonacci numbers $G^{(2)}_{F(n)}(a)$ and $H^{(2)}_{F(n)}(a)$. These numbers are significant as they are related to the consecutive products of the Fibonacci numbers. As a result, we establish consecutive sum-subtraction relations of altered Fibonacci numbers and their Binet-like formulas. Moreover, we explore greatest common divisor (GCD) sequences of r-successive terms of altered Fibonacci numbers represented by $\left\{G^{(2)}_{F(n), r}(a)\right\}$
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Shannon, Anthony G., Özgür Erdağ, and Ömür Deveci. "On the connections between Pell numbers and Fibonacci p-numbers." Notes on Number Theory and Discrete Mathematics 27, no. 1 (2021): 148–60. http://dx.doi.org/10.7546/nntdm.2021.27.1.148-160.

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In this paper, we define the Fibonacci–Pell p-sequence and then we discuss the connection of the Fibonacci–Pell p-sequence with the Pell and Fibonacci p-sequences. Also, we provide a new Binet formula and a new combinatorial representation of the Fibonacci–Pell p-numbers by the aid of the n-th power of the generating matrix of the Fibonacci–Pell p-sequence. Furthermore, we derive relationships between the Fibonacci–Pell p-numbers and their permanent, determinant and sums of certain matrices.
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Howard, Fredric T. "Fibonacci numbers." Mathematical Intelligencer 26, no. 1 (2004): 65. http://dx.doi.org/10.1007/bf02985406.

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Kortezov, Ivaylo. "Double Counting and Fibonacci Numbers." Mathematics and Informatics 67, no. 3 (2024): 336–50. https://doi.org/10.53656/math2024-3-7-dou.

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The article proposes a double counting method for proving combinatorial identities involving Fibonacci numbers. The method is easily remembered by the students. It allows them to apply it creatively in many situations, by (re)discovering the results by themselves and asking meaningful questions. The method is mainly oriented towards preparation for mathematical competitions.
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Wituła, Roman, та Damian Słota. "δ-Fibonacci numbers". Applicable Analysis and Discrete Mathematics 3, № 2 (2009): 310–29. http://dx.doi.org/10.2298/aadm0902310w.

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The scope of the paper is the definition and discussion of the polynomial generalizations of the Fibonacci numbers called here ?-Fibonacci numbers. Many special identities and interesting relations for these new numbers are presented. Also, different connections between ?-Fibonacci numbers and Fibonacci and Lucas numbers are proven in this paper.
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Tasyurdu, Yasemin. "Generalized Fibonacci numbers with five parameters." Thermal Science 26, Spec. issue 2 (2022): 495–505. http://dx.doi.org/10.2298/tsci22s2495t.

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In this paper, we define five parameters generalization of Fibonacci numbers that generalizes Fibonacci, Pell, Modified Pell, Jacobsthal, Narayana, Padovan, k-Fibonacci, k-Pell, Modified k-Pell, k-Jacobsthal numbers and Fibonacci p-numbers, distance Fibonacci numbers, (2, k)-distance Fibonacci numbers, generalized (k, r)-Fibonacci numbers in the distance sense by extending the definition of a distance in the recurrence relation with two parameters and adding three parameters in the definition of this distance, simultaneously. Tiling and combinatorial interpretations of generalized Fibonacci nu
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Szynal-Liana, Anetta, Andrzej Włoch, and Iwona Włoch. "On Types of Distance Fibonacci Numbers Generated by Number Decompositions." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/491591.

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We introduce new types of distance Fibonacci numbers which are closely related with number decompositions. Using special decompositions of the numbernwe give a sequence of identities for them. Moreover, we give matrix generators for distance Fibonacci numbers and their direct formulas.
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Bednarz, Natalia. "On (k,p)-Fibonacci Numbers." Mathematics 9, no. 7 (2021): 727. http://dx.doi.org/10.3390/math9070727.

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In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Fibonacci numbers, Pell numbers, and Narayana numbers, simultaneously. We prove some identities which generalize well-known relations for Fibonacci numbers, Pell numbers and their generalizations. A matrix representation for generalized Fibonacci numbers is given, too.
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Han, Jeong, Hee Kim, and Joseph Neggers. "On Fibonacci functions with Fibonacci numbers." Advances in Difference Equations 2012, no. 1 (2012): 126. http://dx.doi.org/10.1186/1687-1847-2012-126.

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Luca, Florian, and V. Janitzio Mejía Huguet. "Fibonacci-Riesel and Fibonacci-Sierpiński numbers." Fibonacci Quarterly 46-47, no. 3 (2008): 198–201. http://dx.doi.org/10.1080/00150517.2008.12428153.

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Dissertations / Theses on the topic "Fibonacci numbers"

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Fransson, Jonas. "Generalized Fibonacci Series Considered modulo n." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-26844.

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In this thesis we are investigating identities regarding Fibonacci sequences. In particular we are examiningthe so called Pisano period, which is the period for the Fibonacci sequence considered modulo n to repeatitself. The theory shows that it suces to compute Pisano periods for primes. We are also looking atthe same problems for the generalized Pisano period, which can be described as the Pisano period forthe generalized Fibonacci sequence.
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Meinke, Ashley Marie. "Fibonacci Numbers and Associated Matrices." Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1310588704.

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Edson, Marcia Ruth Zamboni Luca Quardo. "Around the Fibonacci numeration system." [Denton, Tex.] : University of North Texas, 2007. http://digital.library.unt.edu/permalink/meta-dc-3676.

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Silva, Bruno Astrolino e. "Números de Fibonacci e números de Lucas." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-03032017-143706/.

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Neste trabalho, exploramos os números de Fibonacci e de Lucas. A maioria dos resultados históricos sobre esses números são apresentados e provados. Ao longo do texto, um grande número de identidades a respeito dos números de Fibonacci e de Lucas são mostradas válidas para todos os inteiros. Sequências generalizadas de Fibonacci, a relação entre os números de Fibonacci e de Lucas com as raízes da equação x2 -x -1 = 0 e a conexão entre os números de Fibonacci e de Lucas com uma classe de matrizes em M2(R) são também exploradas.<br>In this work we explore the Fibonacci and Lucas numbers. The majo
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Heberle, Curtis. "A Combinatorial Approach to $r$-Fibonacci Numbers." Scholarship @ Claremont, 2012. https://scholarship.claremont.edu/hmc_theses/34.

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In this paper we explore generalized “$r$-Fibonacci Numbers” using a combinatorial “tiling” interpretation. This approach allows us to provide simple, intuitive proofs to several identities involving $r$-Fibonacci Numbers presented by F.T. Howard and Curtis Cooper in the August, 2011, issue of the Fibonacci Quarterly. We also explore a connection between the generalized Fibonacci numbers and a generalized form of binomial coefficients.
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Salter, Ena. "Fibonacci vectors." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001244.

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Leonesio, Justin Michael. "Fascinating characteristics and applications of the Fibonacci sequence /." Lynchburg, VA : Liberty University, 2007. http://digitalcommons.liberty.edu.

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Almeida, Edjane Gomes dos Santos. "Propriedades e generalizações dos números de Fibonacci." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7658.

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Edson, Marcia Ruth. "Around the Fibonacci Numeration System." Thesis, University of North Texas, 2007. https://digital.library.unt.edu/ark:/67531/metadc3676/.

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Let 1, 2, 3, 5, 8, … denote the Fibonacci sequence beginning with 1 and 2, and then setting each subsequent number to the sum of the two previous ones. Every positive integer n can be expressed as a sum of distinct Fibonacci numbers in one or more ways. Setting R(n) to be the number of ways n can be written as a sum of distinct Fibonacci numbers, we exhibit certain regularity properties of R(n), one of which is connected to the Euler φ-function. In addition, using a theorem of Fine and Wilf, we give a formula for R(n) in terms of binomial coefficients modulo two.
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Luwes, N. J. "Fibonacci numbers and the golden rule applied in neural networks." Interim : Interdisciplinary Journal: Vol 9, Issue 1: Central University of Technology Free State Bloemfontein, 2010. http://hdl.handle.net/11462/343.

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Published Article<br>In the 13th century an Italian mathematician Fibonacci, also known as Leonardo da Pisa, identified a sequence of numbers that seemed to be repeating and be residing in nature (http://en.wikipedia.org/wiki/Fibonacci) (Kalman, D. et al. 2003: 167). Later a golden ratio was encountered in nature, art and music. This ratio can be seen in the distances in simple geometric figures. It is linked to the Fibonacci numbers by dividing a bigger Fibonacci value by the one just smaller of it. This ratio seems to be settling down to a particular value of 1.618 (http://en.wikipedia.org/w
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Books on the topic "Fibonacci numbers"

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Vorobiev, Nicolai N. Fibonacci Numbers. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8107-4.

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Vorobiev, Nicolai N. Fibonacci Numbers. Birkhäuser Basel, 2002.

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N, Vorobʹev N. Fibonacci numbers. Dover Publications, 2011.

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Bergum, G. E., A. N. Philippou, and A. F. Horadam, eds. Applications of Fibonacci Numbers. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5020-0.

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Bergum, Gerald E., Andreas N. Philippou, and Alwyn F. Horadam, eds. Applications of Fibonacci Numbers. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2058-6.

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Philippou, A. N., A. F. Horadam, and G. E. Bergum, eds. Applications of Fibonacci Numbers. Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-015-7801-1.

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Bergum, Gerald E., Andreas N. Philippou, and Alwyn F. Horadam, eds. Applications of Fibonacci Numbers. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0223-7.

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Howard, Fredric T., ed. Applications of Fibonacci Numbers. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4271-7.

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Bergum, G. E., A. N. Philippou, and A. F. Horadam, eds. Applications of Fibonacci Numbers. Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3586-3.

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Bergum, G. E., A. N. Philippou, and A. F. Horadam, eds. Applications of Fibonacci Numbers. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-1910-5.

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Book chapters on the topic "Fibonacci numbers"

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Vorobiew, Nicolai N. "Number-Theoretic Properties of Fibonacci Numbers." In Fibonacci Numbers. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8107-4_3.

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Lovász, L., J. Pelikán, and K. Vesztergombi. "Fibonacci Numbers." In Discrete Mathematics. Springer New York, 2003. http://dx.doi.org/10.1007/0-387-21777-0_4.

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Vorobiew, Nicolai N. "Introduction." In Fibonacci Numbers. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8107-4_1.

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Vorobiew, Nicolai N. "The Simplest Properties of Fibonacci Numbers." In Fibonacci Numbers. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8107-4_2.

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Vorobiew, Nicolai N. "Fibonacci Numbers and Continued Fractions." In Fibonacci Numbers. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8107-4_4.

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Vorobiew, Nicolai N. "Fibonacci Numbers and Geometry." In Fibonacci Numbers. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8107-4_5.

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Vorobiew, Nicolai N. "Fibonacci Numbers and Search Theory." In Fibonacci Numbers. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8107-4_6.

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Harborth, Heiko, and Arnfried Kemnitz. "Fibonacci Triangles." In Applications of Fibonacci Numbers. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-1910-5_14.

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Matoušek, Jiří. "Fibonacci numbers, quickly." In The Student Mathematical Library. American Mathematical Society, 2010. http://dx.doi.org/10.1090/stml/053/01.

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Moll, Victor. "The Fibonacci numbers." In The Student Mathematical Library. American Mathematical Society, 2012. http://dx.doi.org/10.1090/stml/065/03.

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Conference papers on the topic "Fibonacci numbers"

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Wang, Hsin-Po, and Chi-Wei Chin. "On Counting Subsequences and Higher-Order Fibonacci Numbers." In 2024 IEEE International Symposium on Information Theory (ISIT). IEEE, 2024. http://dx.doi.org/10.1109/isit57864.2024.10619178.

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Timofeev, Evgeniy A., and Alexei Kaltchenko. "Entropy estimation and Fibonacci numbers." In SPIE Defense, Security, and Sensing, edited by Harold H. Szu. SPIE, 2013. http://dx.doi.org/10.1117/12.2016140.

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Rubio-Sánchez, Manuel, and Isidoro Hernán-Losada. "Exploring recursion with fibonacci numbers." In the 12th annual SIGCSE conference. ACM Press, 2007. http://dx.doi.org/10.1145/1268784.1268931.

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Elsner, Carsten, Shun Shimomura, Iekata Shiokawa, and Takao Komatsu. "Reciprocal sums of Fibonacci numbers." In DIOPHANTINE ANALYSIS AND RELATED FIELDS: DARF 2007/2008. AIP, 2008. http://dx.doi.org/10.1063/1.2841913.

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Agaian, Sarkis. "Generalized Fibonacci numbers and applications." In 2009 IEEE International Conference on Systems, Man and Cybernetics - SMC. IEEE, 2009. http://dx.doi.org/10.1109/icsmc.2009.5346744.

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LU, W. T., and F. Y. WU. "GENERALIZED FIBONACCI NUMBERS AND DIMER STATISTICS." In In Celebration of the 80th Birthday of C N Yang. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812791207_0026.

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Shu, Huang. "Generalization of Dedekind Sums Involving Fibonacci Numbers." In 2010 International Conference on Web Information Systems and Mining (WISM). IEEE, 2010. http://dx.doi.org/10.1109/wism.2010.88.

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Fallahpour, Mehdi, and David Megias. "Robust Audio Watermarking Based on Fibonacci Numbers." In 2014 10th International Conference on Mobile Ad-Hoc and Sensor Networks (MSN). IEEE, 2014. http://dx.doi.org/10.1109/msn.2014.58.

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Kulaç, Yıldız, and Murat Tosun. "Some equations on p− complex Fibonacci numbers." In 6TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5020473.

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Zou, Jiancheng, Dongxu Qi, and Rabab K. Ward. "A novel watermarking method based on Fibonacci numbers." In the 2006 ACM international conference. ACM Press, 2006. http://dx.doi.org/10.1145/1128923.1128981.

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Reports on the topic "Fibonacci numbers"

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Swetz, Frank J. Review ofThe Man of Numbers: Fibonacci's Arithmetic Revolution. The MAA Mathematical Sciences Digital Library, 2012. http://dx.doi.org/10.4169/loci003858.

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