Padovan Sequence

The Integer Sequence defined by the Recurrence Relation

$$P(n)=P(n-2)+P(n-3)$$

with the initial conditions $P(0)=P(1)=P(2)=1$. The first few terms are 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, ... (Sloane's A000931). The ratio $\lim_{n\to\infty} P(n)/P(n-1)$ is called the Plastic Constant.

See also Perrin Sequence, Plastic Constant

References

Sloane, N. J. A. Sequence A000931/M0284 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

Stewart, I. ``Tales of a Neglected Number.'' Sci. Amer. 274, 102-103, June 1996.