Y by Adventure10, Mango247
A sequence of integers
is such that
and for
,
![\[a_{n+2}=\left\{\begin{array}{cl}5a_{n+1}-3a_{n}, &\text{if}\ a_n\cdot a_{n+1}\ \text{is even},\\ a_{n+1}-a_{n}, &\text{if}\ a_n\cdot a_{n+1}\ \text{is odd},\end{array}\right. \]](//latex.artofproblemsolving.com/c/f/9/cf9a471f09bbd427d500d054531ce364c3729038.png)
Prove that
for all
.



![\[a_{n+2}=\left\{\begin{array}{cl}5a_{n+1}-3a_{n}, &\text{if}\ a_n\cdot a_{n+1}\ \text{is even},\\ a_{n+1}-a_{n}, &\text{if}\ a_n\cdot a_{n+1}\ \text{is odd},\end{array}\right. \]](http://latex.artofproblemsolving.com/c/f/9/cf9a471f09bbd427d500d054531ce364c3729038.png)
Prove that


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