Fibonacci properties by matrix methods

DOI10.2307/3617892zbMath0416.10004OpenAlexW2802819306MaRDI QIDQ3205307

John R. Silvester

Publication date: 1979

Published in: The Mathematical Gazette (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/3617892

zbMATH Keywords

determinantsmatricesFibonacci sequence

Mathematics Subject Classification ID

Recurrences (11B37) Matrices, determinants in number theory (11C20)

Related Items (16)

On the order-\(m\) generalized Fibonacci \(k\)-numbers ⋮ The (s, t)-Generalized Jacobsthal Matrix Sequences ⋮ More properties of generalized Fibonacci and Lucas numbers ⋮ Automorphisms of some \(K3\) surfaces and Beauville involutions of their Hilbert schemes ⋮ Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography ⋮ Synchronization of chaotic systems using feedback controller: an application to Diffie-Hellman key exchange protocol and elgamal public key cryptosystem ⋮ Matrix structure of Jacobsthal numbers ⋮ An interesting generalized Fibonacci sequence: a two-by-two matrix representation ⋮ A three by three Pascal matrix representations of the generalized Fibonacci and Lucas sequences ⋮ Some new Fibonacci and Lucas identities by matrix methods ⋮ Identities involving generalized Fibonacci-type polynomials ⋮ SOME PROPERTIES OF THE GENERALIZED FIBONACCI SEQUENCE {q_n} BY MATRIX METHODS ⋮ LINEARLIZATION OF GENERALIZED FIBONACCI SEQUENCES ⋮ On the representation of \(k\)-generalized Fibonacci and Lucas numbers ⋮ ON CHARACTERIZATIONS OF SOME LINEAR COMBINATIONS INVOLVING THE MATRICES Q AND R ⋮ Q1 AND Q2 MATRIX REPRESENTATIONS OF GENERALIZED k-FIBONACCI SEQUENCE

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