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?


This is in response to your comment: initial conditions $a_1 = 0.390259$ and $a_2 = 3.64934$
Here's with improved precision (with sufficient error truncation), given the answer provided by Michael.

