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On the (s, t)-Fibonacci and Fibonacci Matrix Sequences.
Ars Comb., 2008It is always fascinating to see what results when seemingly different areas mathematics overlap. This article reveals one such result; number theory and linear algebra are intertwined to yield complex factorizations of the classic Fibonacci, Pell, Jacobsthal, and Mersenne numbers.
Civciv, Hacı, Türkmen, Ramazan
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A note on generalized Fibonacci sequences
Applied Mathematics and Computation, 2011The author proves identities with generalized Fibonacci sequences.
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Acceleration of extended fibonacci sequences
Applied Numerical Mathematics, 1986The authors discuss convergence acceleration of the sequence defined by \(C_ 0=1\), \(C_{n+1}=1+a/C_ n\), \(n=0,1,..\). where a is a nonzero complex number. Some results applying Aitken's \(\Delta^ 2\) process and Shank's transformation to this sequence are given. The rate of convergence is studied showing the superiority of Aitken's process.
Brezinski, C., Lembarki, A.
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The Fibonacci sequence, generalized Fibonacci sequences, and related topics
1995Abstract One of the most engaging puzzles in the history of mathematics was formulated by Leonardo of Pisa, nicknamed Fibonacci (1170-1250) in his celebrated book Liber abaci: How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the ...
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Fibonacci Numbers and Cotangent Sequences
The American Mathematical Monthly, 2002(2002). Fibonacci Numbers and Cotangent Sequences. The American Mathematical Monthly: Vol. 109, No. 7, pp. 655-657.
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A Probabilistic Approach to the Fibonacci Sequence
The Mathematical Intelligencer, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Generalized Fibonacci Sequence
The Fibonacci Quarterly, 1972Fisher, P. S., Kohlbecker, E. E.
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