Find another closed form for this sequence I've recently come across a sequence while doing math which is:
$$\{1;0;2;-1;3;-2;4;-3;...\}$$
And searching for a closed form to express the n-th therm I've came to the following:
$$a_n=1-(-1)^n\lfloor\frac n2\rfloor$$
But I was wondering if there are another closed form not involving the floor (and related) function(s). Can you help me please ?

You can write 
$$\lfloor \frac{n}{2} \rfloor = \frac{n+\frac{(-1)^n-1}{2}}{2}$$
This works because:


*

*If $n=2k$, then you get $k=\frac{2k+0}{2}$

*If $n=2k+1$, then you have $k = \frac{2k+1+(-1)}{2}$


(Moreover, $(-1)^n=\cos(πn)$, if you want to extend this continuously).
In other words:
$$a_n = 1-(-1)^n \left( \frac{n}{2}+\frac{(-1)^n-1}{4} \right) =
\frac{3}{4}+\frac{(-1)^n}{4}(1-2n)$$
Extended by continuity, we get:
$\qquad\qquad\qquad$
