What number comes next in the sequence 0-1-2-4-16?

Answer 1

The differences are not the same so the sequence is not arithmetic.

The sequence starts with a zero, so it cannot be geometric, or an exponential (power) sequence.

The quartic: (2n4 - 19n3 + 64n2 - 83n + 36)/6 fits the 5 points. That gives the next term as 55.

Answer 2

32