Factorizations and representations of the backward second-order linear recurrences (Q869539)
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scientific article; zbMATH DE number 5131553
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Factorizations and representations of the backward second-order linear recurrences |
scientific article; zbMATH DE number 5131553 |
Statements
Factorizations and representations of the backward second-order linear recurrences (English)
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8 March 2007
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Second order linear difference equations with variable coefficients are considered. It is shown that some well-known number sequences such as Fibonacci, Lucas and Pell which can be generated as solutions to these equations are related to determinants and permanents of particular tri-diagonal matrices and also to Chebyshev polynomials. This latter relationship is used to provide representations and factorizations of these numbers.
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second-order linear recurrences
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determinant
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permanent
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factorization
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linear difference equations
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tri-diagonal matrices
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Chebyshev polynomials
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Fibonacci sequence
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Lucas sequence
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Pell sequence
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