1899 asked if there were any counterexamples to this property. The first divisible by composite index n was found only in 1982 by William Adams and Daniel Shanks. They presented a detailed investigation of the sequence, with a sequel appearing four years later.

Properties

The Perrin sequence also satisfies the recurrence relation Starting from this and the defining recurrence, one can create an infinite number of further relations, for example

The generating function

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