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Alternating generalized Fibonacci sequences [PDF]
Notes on Number Theory and Discrete MathematicsIn a recent paper, K.~T. Atanassov and A.~G. Shannon introduced a Fibonacci-like sequence derived from the generalized Fibonacci sequence by incorporating alternating signs into the recurrence relation.
Carlos M. da Fonseca, Paulo Saraiva
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On Third-Order Bronze Fibonacci Numbers
Mathematics, 2021 In this study, we firstly obtain De Moivre-type identities for the second-order Bronze Fibonacci sequences. Next, we construct and define the third-order Bronze Fibonacci, third-order Bronze Lucas and modified third-order Bronze Fibonacci sequences. Then,
Mücahit Akbiyik, Jeta Alo
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Factorizations of the Fibonacci Infinite Word [PDF]
, 2015 The aim of this note is to survey the factorizations of the Fibonacci infinite word that make use of the Fibonacci words and other related words, and to show that all these factorizations can be easily derived in sequence starting from elementary ...
Fici, Gabriele
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Gap Sequence of Factors of Fibonacci Sequence
, 2014 Let w be a factor of Fibonacci sequence F=x_1x_2..., then it appears in the sequence infinitely many times. Let w_p be the p-th appearance of w and v_{w,p} be the gap between w_p and w_{p+1}.
Huang, Yuke, Wen, Zhiying
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Generalized Fibonacci sequences in groupoids [PDF]
Advances in Difference Equations, 2013 Abstract In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents. Using the notion of Smarandache-type P-algebra, we obtain several relations on groupoids which are derived from generalized Fibonacci ...
Kim, Hee, Neggers, J, So, Keum
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Journal of Magnetic Resonance Imaging, Volume 63, Issue 5, Page 1435-1447, May 2026.ABSTRACT Background Non‐contrast renal MR angiography (MRA) is valuable for patients who cannot receive contrast agents or when avoiding radiation is desired. However, the conventional inflow inversion recovery (IFIR) method is limited by incomplete background suppression, venous contamination, and motion sensitivity.
Yulin Wang +13 more
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From Fibonacci to the mathematics of cows and quantum circuitry [PDF]
, 2014 The Fibonacci sequence is a famously well-known integer sequence from the thirteenth century which has transcended its original motivation. It possesses many interested and varied applications within architecture, engineering and science. Less well known
Wilmott, CM
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, 2017 A numerical semigroup is an additive submonoid of the natural numbers with finite complement. The size of the complement is called the genus of the semigroup. How many numerical semigroups have genus equal to $g$?
Kaplan, Nathan
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Magnetic Resonance in Medicine, Volume 95, Issue 5, Page 2627-2643, May 2026.ABSTRACT Purpose To design 3D radial spiral phyllotaxis trajectories aimed at removing phase inconsistencies, improving image quality, and enhancing parametric mapping accuracy by acquiring nearly opposing spokes starting from both hemispheres in 3D radial k‐space. Methods Two 3D radial trajectories, pole‐to‐pole and continuous spiral phyllotaxis, were
Eva S. Peper +12 more
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Fibonacci words in hyperbolic Pascal triangles
, 2017 The hyperbolic Pascal triangle ${\cal HPT}_{4,q}$ $(q\ge5)$ is a new mathematical construction, which is a geometrical generalization of Pascal's arithmetical triangle.
Németh, László
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