February 22nd, 2017, 05:32 PM  #11 
Newbie Joined: Aug 2015 From: china Posts: 6 Thanks: 4 
In fact, it is a recursive problem. Known $\displaystyle f(0)=1,f(1)=1,f(n)=f(n1)+f(n2)$ One obtains $\displaystyle f(n)=(\frac{\sqrt{5}+1}{2})^n+(\frac{\sqrt{5}1}{2})^n$ Similarly Known $\displaystyle f(0)=2,f(1)=6,f(n)=3f(n1)f(n2)$ One obtains $\displaystyle f(n)=(\frac{3+\sqrt{5}}{2})^n+(\frac{3\sqrt{5}}{2})^n=(\frac{\sqrt{5}+1}{2})^{2n}+(\frac {\sqrt{5}1}{2})^{2n}$ 

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