Recurrence Relations
In the spiral, each triangle shares a side with two others giving a visual proof that the Padovan sequence also satisfies the recurrence relation
Starting from this, the defining recurrence and other recurrences as they are discovered, one can create an infinite number of further recurrences by repeatedly replacing by
The Perrin sequence satisfies the same recurrence relations as the Padovan sequence, although it has different initial values. This is a property of recurrence relations.
The Perrin sequence can be obtained from the Padovan sequence by the following formula:
Read more about this topic: Padovan Sequence
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