It looks like there are two patterns.
Look at the odd numbered slots:
8, 4, 0, -4, -8
Just subtract 4 each time.
That pattern will continue like this:
8, 4, 0, -4, -8, -12, -16, -20 and so on
Now look at the even numbered slots:
7, 11, 15, 19
Just add 4 each time.
That pattern will continue like this:
7, 11, 15, 19, 23, 27, 31 and so on
So the overall pattern (8, 7, 4, 11, 0, 15, -4, 19, -8) will continue like this:
8, 7, 4, 11, 0, 15, -4, 19, -8, 23, -12, 27, -16, 31, -20, 35 and so on