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.

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Keywords Characteristic polynomials, Conditional recurrences, Continuants, Fibonacci sequences, Integer partitions, Linear recurrences
Persistent URL dx.doi.org/10.1016/j.amc.2014.05.108
Journal Applied Mathematics and Computation
Citation
Panario, D. (Daniel), Sahin, M. (Murat), Wang, Q, & Webb, W. (William). (2014). General conditional recurrences. Applied Mathematics and Computation, 243, 220–231. doi:10.1016/j.amc.2014.05.108