Assigning a formula for the general term of a sequence Is it possible to find a formula for the general term of the sequence 
$$\{s_n\}_{n=0}^{n=\infty}=(1,-2,6,-8,15,-18,28,-32,45,-50,66,-72,\ldots)\text{ ?}$$
 A: Yes: it’s two simpler sequences interwoven. You have
$$\langle s_{2n}:n\in\Bbb N\rangle=\langle 1,6,15,28,45,66,\ldots\rangle$$
and
$$\langle s_{2n+1}:n\in\Bbb N\rangle=\langle -2,-8,-18,-32,-50,-72,\ldots\rangle\;.$$
Each subsequence has second difference $4$, so both subsequences are quadratic, and it’s a routine exercise to extract the appropriate quadratic expression. Thus, at worst you get a two-part definition.
In fact we find that $$a_{2n}=2n^2+3n+1$$ and $$a_{2n+1}=-(2n^2+4n+2)=-\big(n(2n+1)+(2n+1)+n+1\big)\;,$$ so in general we have
$$\begin{align*}
a_n&=(-1)^n\left(n\left\lfloor\frac{n}2\right\rfloor+n+\left\lfloor\frac{n}2\right\rfloor+1\right)\\
&=(-1)^n(n+1)\left(\left\lfloor\frac{n}2\right\rfloor+1\right)\;.
\end{align*}$$
A: Not without context, no. We could simply interpolate some foul polynomial out of those points, unless there are more restrictions given.
Still, your sequence seems to be a decent match for http://oeis.org/A093005, though with a factor of $(-1)^i$ on the $i^{th}$ term.
