Let $n\ge 2r$ be positive integers.  

Is there a closed form for following finite summation involving in q-binomial coefficients 
$$\sum\_{s=0}^r(-1)^sq^{\frac{s(s+1)}{2}}{n-2r+s\brack n-2r}\_q{n\brack r-s}\_q\,\,\,\,\,\, ?$$ 
I found this while studying q-Fibonacci/ Lucas polynomials.  

What is the general approach for evaluating this type of series?  

Any suggestion would be appreciated. 



What is the value of this sum involving q-binomials?
Doron Zeilberger has written a Maple code for checking and proving [ordinary binomial identities](http://www.math.rutgers.edu/~zeilberg/tokhniot/EKHAD) and their $q$-analogues. What you need in the present case is the package called [qEKHAD](http://www.math.rutgers.edu/~zeilberg/tokhniot/qEKHAD).


I just tested your sum and it leads to a quadratic recurrence in $r$, so you may not expect a closed form as an answer. The lucky cases are linear recurrences in the "external" parameter (here, it is $r$). The latter situation fits the so-called [Wilf-Zeilberger pair](https://en.wikipedia.org/wiki/Wilf%E2%80%93Zeilberger_pair).


I also sought for other factors $q^{\mu(s)}$ instead of $q^{\binom{s+1}2}$, none of the usual suspects lead to a closed form. Sorry.


