Mr. Fantastic did his usual excellent job.
I too enjoy cranking out the generating functions for these problems.
However, since it asked for the next term (only),
. . we can use a somewhat intuitive approach.
What number comes next in this series: .
Take the difference of consecutive terms.
Then take the differences of the differences, and so on.
It seems that the 3rd differences are constant.
If this is true, we can extend the diagram to the right . . .
We assume that the next 3rd difference is also 8:
Then the next 2nd difference must be 28:
Then the next 1st difference must be 71:
Finally, the next term of the sequence must be 158:
. . ta-DAA!