Construct a recurrence relation with initial terms $a_{0}=1$, $a_{1}=0$, $a_{2}=0$ and $a_{n}=a_{n-3}+a_{n-2}$ for $n>2$. The first few terms of the sequence defined by this recurrence relation are: 1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151 (listed in A000931 of Sloane’s OEIS). This is the , named after mathematician Richard Padovan. Its generating function is
 $G(a(n);x)=\frac{1-x^{2}}{1-x^{2}-x^{3}}$
The $n$th Padovan number asymptotically matches the $n$th power of the plastic constant.