Extension To Negative Parameters
As with any sequence defined by a recurrence relation, Padovan numbers P(m) for m<0 can be defined by rewriting the recurrence relation as
Starting with m=-1 and working backwards, we extend P(m) to negative indices:
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P−20 P−19 P−18 P−17 P−16 P−15 P−14 P−13 P−12 P−11 P-10 P-9 P-8 P-7 P-6 P-5 P-4 P-3 P-2 P-1 P0 P1 P2 7 -7 4 0 −3 4 −3 1 1 -2 2 -1 0 1 -1 1 0 0 1 0 1 1 1
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