Factorizations and representations of the backward second-order linear recurrences

DOI10.1016/j.cam.2006.02.012zbMath1115.39004OpenAlexW2156688422WikidataQ114202162 ScholiaQ114202162MaRDI QIDQ869539

Dursun Tasci, Emrah Kılıç

Publication date: 8 March 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.02.012

zbMATH Keywords

Chebyshev polynomialsfactorizationdeterminantFibonacci sequencepermanentlinear difference equationsLucas sequencePell sequencesecond-order linear recurrencestri-diagonal matrices

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Recurrences (11B37) Additive difference equations (39A10) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (7)

On a constant-diagonals matrix ⋮ Sums of the squares of terms of sequence \(\{u_n\}\) ⋮ A computational algorithm for special \(n\)th-order pentadiagonal Toeplitz determinants ⋮ An analytical approach: explicit inverses of periodic tridiagonal matrices ⋮ Explicit formula for the inverse of a tridiagonal matrix by backward continued fractions ⋮ Positive integer powers of certain complex tridiagonal matrices ⋮ Explicit eigenvalues of some perturbed heptadiagonal matrices via recurrent sequences

Cites Work

• On the order-\(k\) generalized Lucas numbers
• On the generalized order-\(k\) Fibonacci and Lucas numbers
• On the permanents of some tridiagonal matrices with applications to the Fibonacci and Lucas numbers
• The Discrete Cosine Transform
• The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms
• Fibonacci Determinants
• Permanents of (0, 1)-Circulants
• Matrix theory. Basic results and techniques
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