Results 111 to 120 of about 3,254,389 (231)
Elementary sequences, sub-Fibonacci sequences
Discrete Applied Mathematics, 1993 A nondecreasing integer sequence \(x_ 1,x_ 2,\dots,x_ k\) with \(x_ 1=x_ 2=1\) and \(n \geq 2\) is said to be elementary if for all \(k \leq n\) \((x_ k>1 \Rightarrow x_ k=x_ i+x_ j\) for some \(i \neq j)\) and sub- Fibonacci if for all \(k \in \{3,\dots,n\}\) \((x_ k \leq x_{k-1}+x_{k- 2})\).
Fishburn, Peter C., Roberts, Fred S.
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The Fibonacci Sequence: Nature’s Little Secret
, 2014 Fibonacci: a natural design, easy to recognise - yet difficult to understand. Why do flowers and plants grow in such a way? It comes down to nature's sequential secret…This paper discusses how and when the Fibonacci sequence occurs in flora.
Nikoletta Minarova
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(±1)-Invariant sequences and truncated Fibonacci sequences
Linear Algebra and its Applications, 2005 Let \(P\) and \(D\) denote the Pascal matrix \(\bigl[\binom{i}{j}\bigr]\), (\(i,j=0,1,2,\dots\)) and the diagonal matrix \(\text{diag}((-1)^0,(-1)^1,(-1)^2,\dots)\), respectively. An infinite-dimensional real vector \(\mathbf x\) is called a \(\lambda\)-invariant sequence if \(PD\mathbf x=\lambda\mathbf x\).
Choi, Gyoung-Sik +3 more
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On Some Identities for k-Fibonacci Sequence
, 2014 We obtain some identities for k-Fibonacci numbers by using its Binet’s formula. Also, another expression for the general term of the sequence, using the ordinary generating function, is provided.
P. Catarino
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Journal of Inequalities and ApplicationsIn the context of modular function spaces, we propose and investigate the Fibonacci-Ishikawa iteration method applied to non-expansive, asymptotically monotonic mathematical operators.
Anita Tomar +4 more
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Explosive Fibonacci-sequence growth into unusual sector-face morphology in poly(L-lactic acid) crystallized with polymeric diluents. [PDF]
Sci Rep, 2020 Lugito G, Nagarajan S, Woo EM.
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Generalized Fibonacci Sequences and Binet-Fibonacci Curves
, 2017 We have studied several generalizations of Fibonacci sequences as the sequences with arbitrary initial values, the addition of two and more Fibonacci subsequences and Fibonacci polynomials with arbitrary bases. For Fibonacci numbers with congruent indices we derived general formula in terms of generalized Fibonacci polynomials and Lucas numbers.
Özvatan, Merve, Pashaev, Oktay K.
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IDENTITIES FOR MULTIPLICATIVE COUPLED FIBONACCI SEQUENCES OF RTH ORDER
Journal of New Theory, 2017 Abstaract−Many author studied coupled Fibonacci sequences and multiplicative coupled Fi- bonacci sequences of lower order two, three and four etc. In this paper we defined multiplicative coupled Fibonacci Sequences of rthorder under 2rdifferent schemes ...
Ashok Dnyandeo Godase, Macchindra Dhakne
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On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces
Communications in Advanced Mathematical SciencesIn this work, we give some results about the basic properties of the vector-valued Fibonacci sequence spaces. In general, sequence spaces with Banach space-valued cannot have a Schauder Basis unless the terms of the sequences are complex or real terms ...
Seçkin Yalçın, Yılmaz Yılmaz
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A MATRIX REPRESENTATION OF A GENERALIZED FIBONACCI POLYNOMIAL
Journal of New Theory, 2017 The Fibonacci polynomial Fn(x) defined recurrently by Fn+1(x) = xFn(x)+Fn−1(x), with F0(x) = 0, F1(0) = 1, for n ≥ 1 is the topic of wide interest for many years. In this article, generalized Fibonacci polynomials Fbn+1(x) and Lbn+1(x) are introduced and
A. D. Godase, M. B. Dhakne
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