Find a formula of sequence: $\frac{-1}{2}, 0, \frac{1}{10}, 0, \frac{-1}{26}, 0, \frac{1}{50}, 0, \frac{-1}{82}, 0, \frac{1}{122}, 0, \dots$ I'm working on a discrete math homework that finding a formula for the following sequence:

$$\frac{-1}{2}, 0, \frac{1}{10}, 0, \frac{-1}{26}, 0, \frac{1}{50}, 0, \frac{-1}{82}, 0, \frac{1}{122}, 0, \dots$$

I've tried but can't find the same difference between those numbers.

I come up with something as: $\frac{1}{2}((-1)^{(x-1)}-1)\times0.5\times0.2$
But it's not anywhere close as I mentioned, I don't know the difference.

Also, is there way to apply to find formula for this kind of problem.

Thank you so much.
Hint: Consider the sequence
\begin{eqnarray*}
2(n^2+(n+1)^2).
\end{eqnarray*}
Hint: Consider the sequence
\begin{eqnarray*}
2(n^2+(n+1)^2).
\end{eqnarray*}