##### 斐波那契数 - 斐波那契数 - **斐波那契数**是递归[[计数序列]]的经典代表 $0,1,1,2,3,5,8,13,21,34,55,89,144$ - $F_0 = 0$, $F_1 = 1$, $F_n = F_{n-1} + F_{n-2}$ - $\displaystyle F_n=\frac{\phi^n-\psi^n}{\sqrt{5}}$, $\displaystyle \phi = \frac{1+\sqrt{5}}{2}$, $\displaystyle \psi = \frac{1-\sqrt{5}}{2}$ - $\displaystyle G(x)=\frac{x}{1-x-x^2}=\sum^{\infty}_{n=0}F_nx^n$