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On multiperiodic infinite recursions and their finite core. (English) Zbl 1217.05020

Summary: We define multiperiodic infinite recursions and show that for such a recursion there is a finite linear recursion, the finite core, which gives almost the same type of recursion except for a different offset. Moreover, if we add the sequences produced by all multiperiodic infinite recursions with a given finite core, we almost obtain a multiple of the sequence associated with the finite core.

MSC:

05A15 Exact enumeration problems, generating functions
05A17 Combinatorial aspects of partitions of integers
05A19 Combinatorial identities, bijective combinatorics
11P81 Elementary theory of partitions
11P83 Partitions; congruences and congruential restrictions

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Online Encyclopedia of Integer Sequences:

Expansion of 1/(1-x^2-x^3-x^6).