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.

05A15, 05A17, 05A19, 11P81, 11P83

periodic infinite recursion, unordered additive partition, linear recurrence, sequence function, multiperiodicity, Fibonacci number