Factorizations and representations of second order linear recurrences with indices in arithmetic progressions

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Authors
Kilic, Emrah
Stănică, Pantelimon
Subjects
second order recurrences
factorizations
matrices
determinants
generating functions
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Date of Issue
2009
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Abstract
In this paper we consider second order recurrences (Vk) and (Un). We give second order linear recurrences for the sequences (V+kn) and U+kn). Using these recurrence relations, we derive relationships between the deteminants of certain matrices and these sequences. Further, as genralizations of the earlier resutls, we give representations and trigonometric factorizations of these sequences by matrix methods and methods relying on Chebyshev polynomials of the first and second kinds. We give the generating functions and some combinatorial representation of these sequences.
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https://hdl.handle.net/10945/38828
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Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
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Citation
Bulletin Mex. Math. Soc. 15 (2009), 23-36.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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