Recurrence relation solution $a_{n}=\frac{a_{n-1}}{a_{n-1}-a_{n-2}}$ I want to find the analytic form of the recurrence relation $$a_{n}=\frac{a_{n-1}}{a_{n-1}-a_{n-2}},\,a_{1}=2,\,a_{2}=1 $$ but when looking at the results they seem chaotic. Is it possible that it simply doesn't have any analytic form?

It seems to be chaotic I calculated and plotted the first 60 points of the solution.

If there was a solution it would have to have some periodic tendancies but it seems chaotic where these tendencies are and has unpredictable spikes well above the range of a normal Sin or Cos function. 
