Results 71 to 80 of about 702 (172)
Algebraic and Probabilistic Aspects of Some Binary Recurrence Sequences
, 2023 Since its discovery in the year 1999, the sequence of balancing numbers (also known as the balancing sequence) has been motivating researchers to work on many algebraic and analytic properties associated with it.
Patra, Asim
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On the generalized Gaussian Fibonacci numbers
, 2017 Many authors define certain generalizations of the usual Fibonacci, Pell and Lucas numbers by matrix methods and then obtain the Binet formulas and combinatorial representations of the generalizations of these number sequence.
Lee, G.Y., Aşçı, Mustafa
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Generalized Gaussian Fibonacci numbers and sums by matrix methods
, 2017 Many authors define certain generalizations of the usual Fibonacci, Pell and Lucas numbers by matrix methods and then obtain the Binet formulas and combinatorial representations of the generalizations of these number sequence.
Aşcı, Mustafa, Lee, G.Y.
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, 2020 A Lucas sequence is a binary recurrence sequences that includes as special cases, the Pell, the associatedPell, the balancing, the Lucasbalancing, the balancinglike and the associated balancinglike sequences.
Sahukar, Manasi Kumari
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Generalized Version of the Characteristic Number of Two Simultaneous Pell's Equations
Rocky Mountain Journal of Mathematics, 2006 Given the integers \(D,N\), where \(D\) is positive and not a perfect square, it is a well known classical fact that all integer solutions \((U,V)\) of the equation \(U^2-DV^2=N\) are obtained by means of the relation \(U_n+V_n\sqrt{D}=(u+v\sqrt{D})(a+b\sqrt{D})^n\), where \((a,b)\) is the fundamental solution of the Pell equation \(x^2-Dy^2=1\), while
openaire +3 more sources
Generalization of some known number sequences
, 2009 Bu çalışma üç bölümden oluşmaktadır. İlk bölümde günümüz bilim insanlarının ilgisini çeken Fibonacci, Pell, Lucas ve Jacobsthal sayı dizilerinin tanımları ve bilinen bazı özellikleri verilip, bu dizilerle ilgili olarak tanımlanan genelleştirilmiş sayı ...
Yılmaz, Fatih
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, 2023 Undeniably, optimization problems of smooth functions have been extensively investigated by many researchers with the use of calculus throughout the years.
Chong, Chin Yoon *
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Proofs of some generalized fibonacci identities based on laplace expansion formula
, 2014 Bu çalışmada, Fibonacci, Pell ve Jacobsthal sayı dizilerinin bir genelleştirmesi olan, genelleştirilmiş Fibonacci dizisi için farklı iki özdeşlik, üçlü bant matris dizisinin determinantlarında Laplace açılım formülü kullanılarak ispatlanmıştır. Fibonacci
Yaşar, Meral
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Sum of Consecutive Terms of Pell and Related Sequences
We study new identities related to the sums of adjacent terms in the Pell sequence, defined by $P_{n} := 2P_{n-1}+P_{n-2}$ for $ n\geq 2$ and $P_{0}=0, P_{1}=1$, and generalize these identities for many similar sequences.
Anand, Navvye +5 more
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