Results 181 to 190 of about 613 (205)
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On the Binomial Sums of k-Fibonacci and k -Lucas sequences
AIP Conference Proceedings, 2011The main purpose of this paper is to establish some new properties of k‐Fibonacci and k‐Lucas numbers in terms of binomial sums. By that, we can obtain these special numbers in a new and direct way. Moreover, some connections between k‐Fibonacci and k‐Lucas numbers are revealed to get a more strong result.
N. Yilmaz +7 more
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Integration Sequences of Fibonacci and Lucas Polynomials
1993Let us consider the Fibonacci polynomials U n (x)= W n (0,1; x, - 1) and the Lucas polynomials V n (x) = W n (2,x; x, - 1) (See [6] and [7] for background material on the sequences W n ) defined as $$ {U_n}(x) = x{U_{{n - 1}}}(x) + {U_{{n - 2}}}(x)\;\;\left[ {{U_0}(x) = 0,\;{U_1}(x) = 1} \right] $$ (1.1) and $$ {V_n}(x) = x{V_{{n - 1}}}(x)
Alwyn F. Horadam, Piero Filipponi
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FIBONACCI AND LUCAS SEQUENCES AS THE PRINCIPAL MINORS OF SOME INFINITE MATRICES
Journal of Algebra and Its Applications, 2009In the literature one may encounter certain infinite tridiagonal matrices, the principal minors of which, constitute the Fibonacci or Lucas sequence. The major purpose of this article is to find new infinite matrices with this property. It is interesting to mention that the matrices found are not tridiagonal which have been investigated before ...
Moghaddamfar, A. R. +3 more
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Integer sequences that behave as Fibonacci-Lucas pairs
The Mathematical Gazette, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Some Subsequences of the Generalized Fibonacci and Lucas Sequences
2019We derive first-order nonlinear homogeneous recurrence relations for certain subsequences of generalized Fibonacci and Lucas sequences. We also present a polynomial representation for the terms of Lucas subsequence.
Kılıç, Emrah, Kılıç, Elif Tan
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A q-analogue of the bi-periodic Fibonacci and Lucas sequences and Rogers–Ramanujan Identities
Ramanujan Journal, 2022Nassima Belaggoun +2 more
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k-Fibonacci and k-Lucas Numbers as Product of Two Repdigits
Results in Mathematics, 2021Salah Eddine Rihane, Rihane Salah Eddine
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On Concatenations of Fibonacci and Lucas Numbers
Bulletin of the Iranian Mathematical Society, 2022Murat Alan
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Second Derivative Sequences of Fibonacci and Lucas Polynomials
The Fibonacci Quarterly, 1993Piero Filipponi, Alwyn F. Horadam
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