Generalization of an identity involving the generalized Fibonacci numbers and its applications.
Mohammad Farrokhi, D.G. (2009)
Integers
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Displaying similar documents to “Some trigonometric identities involving Fibonacci and Lucas numbers.”
Generalization of an identity involving the generalized Fibonacci numbers and its applications.
A generalization of the Cassini formula
Alexey Stakhov (2012)
Visual Mathematics
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Gelin-Cesáro identities for Fibonacci and Lucas quaternions
Ahmet Daşdemir (2019)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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To date, many identities of different quaternions, including the Fibonacci and Lucas quaternions, have been investigated. In this study, we present Gelin-Cesáro identities for Fibonacci and Lucas quaternions. The identities are a worthy addition to the literature. Moreover, we give Catalan's identity for the Lucas quaternions.
On binomial sums for the general second order linear recurrence.
Kiliç, Emrah, Tan, Elif (2010)
Integers
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An inequality for Fibonacci numbers
Horst Alzer, Florian Luca (2022)
Mathematica Bohemica
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We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.
On the number of independent sets in a tree.
Law, Hiu-Fai (2010)
The Electronic Journal of Combinatorics [electronic only]
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Self-describing sequences and the Catalan family tree.
Šuniḱ, Zoran (2003)
The Electronic Journal of Combinatorics [electronic only]
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Fibonacci and Telephone Numbers in Extremal Trees
Urszula Bednarz, Iwona Włoch (2018)
Discussiones Mathematicae Graph Theory
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In this paper we shall show applications of the Fibonacci numbers in edge-coloured trees. In particular we determine the successive extremal graphs in the class of trees with respect to the number of (A, 2B)-edge colourings. We show connections between these numbers and Fibonacci numbers as well as the telephone numbers.
From paths to stars.
Alameddine, A.F. (1991)
International Journal of Mathematics and Mathematical Sciences
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Higher-order Lucas numbers.
Randic, M., Morales, D., Araujo, O. (2008)
Divulgaciones Matemáticas
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Balanced integral trees
Pavol Híc, Roman Nedela (1998)
Mathematica Slovaca
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Note: Sharp Upper and Lower Bounds on the Number of Spanning Trees in Cartesian Product of Graphs
Jernej Azarija (2013)
Discussiones Mathematicae Graph Theory
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Let G1 and G2 be simple graphs and let n1 = |V (G1)|, m1 = |E(G1)|, n2 = |V (G2)| and m2 = |E(G2)|. In this paper we derive sharp upper and lower bounds for the number of spanning trees τ in the Cartesian product G1 □G2 of G1 and G2. We show that: [...] and [...] . We also characterize the graphs for which equality holds. As a by-product we derive a formula for the number of spanning trees in Kn1 □Kn2 which turns out to be [...] .