Results 31 to 40 of about 2,413 (223)

Identities relating six members of the Fibonacci family of sequences

Karpatsʹkì Matematičnì Publìkacìï, 2022
In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences.
R. Frontczak, T. Goy, M. Shattuck
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The Fibonacci-circulant sequences in the binary polyhedral groups [PDF]

International Journal of Group Theory, 2021
In 2017 Deveci et al‎. ‎defined the Fibonacci-circulant sequences of the first and second kinds as shown‎, ‎respectively:‎x_n^1 = -x_(n-1)^1+x_(n-2)^1-x_(n-3)^1 for n≥4,where x_1^1=x_2^1=0 and x_3^1=1andx_n^2 = -x_(n-3)^2-x_(n-4)^2+x_(n-5)^2 for n≥6 ...
Erdal Karaduman, Omur Deveci
doaj   +1 more source

On Certain Power Horadam Sequences

Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2022
In this study, firstly, we analyzed power Fibonacci sequences defined by Ide and Renault in [13]. Then, we described two power Horadam sequences modulo s for u=1,v=3 and u=3,v=1, respectively. We determined those modulus s for which the two power Horadam
Çağla Çelemoğlu, Selime Beyza Özçevik, Şenol Eren   +2 more
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Algebraic divisibility sequences over function fields [PDF]

, 2011
In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields ...
Mahe, Valery, Ingram, Patrick, Valéry Mahé, Marco Streng, Streng, T.C., Patrick Ingram, Streng, Marco, Katherine E. Stange, Stange, K.E., Silverman, Joseph H., Mahé, V., Joseph H. Silverman, Silverman, J.H., Ingram, P., Stange, Katherine E.   +14 more
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Power Fibonacci sequences in quadratic integer modulo m [PDF]

Notes on Number Theory and Discrete Mathematics
The power Fibonacci sequence in ℤₘ[√δ] is defined as a Fibonacci sequence Fₙ=Fₙ₋₁+Fₙ₋₂ where F₀=1 and F₁=a, such that a∈ℤₘ[√δ] and Fₙ≡aⁿ(mod m), for all n∈ℕ∪{0}. In this paper, we investigated the existence of power Fibonacci sequences in ℤₘ[√δ], and the
Paul Ryan A. Longhas, Cyryn Jade L. Prendol, Jenelyn F. Bantilan, Larra L. De Leon   +3 more
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Complete k-ary trees and generalized meta-Fibonacci sequences [PDF]

Discrete Mathematics & Theoretical Computer Science, 2006
We show that a family of generalized meta-Fibonacci sequences arise when counting the number of leaves at the largest level in certain infinite sequences of k-ary trees and restricted compositions of an integer.
Chris Deugau, Frank Ruskey
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Accelerations of generalized Fibonacci sequences

The Fibonacci Quarterly, 2011
In this paper we study how to accelerate the convergence of the ratios (x_n) of generalized Fibonacci sequences. In particular, we provide recurrent formulas in order to generate subsequences (x_{g_n}) for every linear recurrent sequence (g_n) of order 2.
ABRATE, MARCO, MURRU, NADIR, Cerruti U, BARBERO, STEFANO   +3 more
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Note on a Fibonacci parity sequence

Cryptography and Communications, 2022
Let ftm = 0111010010001... be the analogue of the Thue-Morse sequence in Fibonacci representation. In this note we show how, using the Walnut theorem-prover, to obtain a measure of its complexity, previously studied by Jamet, Popoli, and Stoll. We strengthen one of their theorems and disprove one of their conjectures.
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Generalized Fibonacci-like sequence and Fibonacci sequence

International Journal of Contemporary Mathematical Sciences, 2014
Every term in the Fibonacci Sequence can be determined recursively with the help of initial values F0 = 0, F1 = 1. Similar is the case with Lucas Sequence. In this paper, we study Generalized Fibonacci-Like sequence {Dn} defined by the recurrence relation Dn = Dn-1 + Dn-2, for all n  2 with D0 = 2 and D1 = 1+m, m being a fixed positive integer.
Sanjay Harne, Bijendra Singh, Shubhraj Pal   +2 more
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Trees and Meta-Fibonacci Sequences [PDF]

The Electronic Journal of Combinatorics, 2009
For $k>1$ and nonnegative integer parameters $a_p, b_p$, $p = 1..k$, we analyze the solutions to the meta-Fibonacci recursion $C(n)=\sum_{p=1}^k C(n-a_p-C(n-b_p))$, where the parameters $a_p, b_p$, $p = 1..k$ satisfy a specific constraint. For $k=2$ we present compelling empirical evidence that solutions exist only for two particular families of ...
Abraham Isgur, David Reiss, Stephen M. Tanny   +2 more
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