General conditional recurrences
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摘要
A general conditional recurrence sequence {qn} 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 {qn} satisfies a single recurrence equation not dependent on the modulus r. We also obtain generating functions and Binet-like formulas for such sequences.
论文关键词：Linear recurrences,Characteristic polynomials,Conditional recurrences,Continuants,Fibonacci sequences,Integer partitions
论文评审过程：Available online 21 June 2014.
论文官网地址：https://doi.org/10.1016/j.amc.2014.05.108
