Exact Perrin Number Calculator

Use P(0) = 3, P(1) = 0, and P(2) = 2, then calculate P(n) = P(n-2) + P(n-3) from index three onward. The seed triple, not only the recurrence, identifies the Perrin sequence. Inputs must be whole numbers inside the displayed domain; the page never rounds a decimal into an accepted index. This ties the answer to one explicit convention instead of silently mixing sequence offsets or combinatorial interpretations.

Perrin and Padovan numbers share a recurrence but their different seeds create different canonical sequences. Generate the ordered terms and inspect the final two source positions. Recompute the displayed recurrence or closed form with the same inputs and compare its previous terms or counting factors. That check supports this bounded result, but it does not transfer the interpretation to a different sequence or counting object.

The index is capped at 100 so terms remain exact and computation stays bounded. The conservative bound keeps each displayed integer trustworthy. Combinatorial and recurrence values can grow rapidly even when the inputs look small. The conservative cap prevents browser stalls and avoids presenting an unsafe floating-point integer as exact; larger work needs arbitrary-precision software and independent resource controls.