Exact Padovan Number Calculator

Use P(0) = P(1) = P(2) = 1, then calculate P(n) = P(n-2) + P(n-3) for each index from three onward. Publishing all three starting values prevents an off-by-one convention mismatch. 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.

Padovan references can shift indexing; the three displayed seeds determine exactly which term this page reports. Write the terms in order and add the entries two and three places back. 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 to preserve exact integer output and bounded work. The cap safely contains this slower-growing recurrence. 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.