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General conditional recurrences
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DOI：10.1016/j.amc.2014.05.108.png)
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Abstract
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A general conditional recurrence sequence {q(n)} is one in which the recurrence satisfied by qn depends on the residue of n modulo some integer r >= 2. The properties of such sequences are studied, and in particular it is shown that any such sequence {q(n)} satisfies a single recurrence equation not dependent on the modulus r. We also obtain generating functions and Binet-like formulas for such sequences. (C) 2014 Elsevier Inc. All rights reserved.
Keywords:
Linear recurrences
Characteristic polynomials
Conditional recurrences
Continuants
Fibonacci sequences
Integer partitions
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