4
The next term is -2.
4
16 is the next number. All you do is sequentially add the next odd number. Therfore after 16 the next number would be 25... the next 36... the next 49... the next 54...
add 2, add 4, take away 3. I don't know if it has a name.
8 (again) The sequence is generated by t(n) = (-n3 + 6n2 + 7n - 12)/6 for n = 1, 2, 3, ...
The next term is -2.
4
312 211 110 3-1=2 2-1=1 1-1=0
The sequence represents the number of line segment ends in the previous letter. A,2,B,0,C,2,D,0,E,3,F,3,G,2,H,4,I,4,J,(2 or 3, depending on how it is written) and so on.
12
4
16 is the next number. All you do is sequentially add the next odd number. Therfore after 16 the next number would be 25... the next 36... the next 49... the next 54...
add 2, add 4, take away 3. I don't know if it has a name.
5.
The next number in the sequence is 48.
8 (again) The sequence is generated by t(n) = (-n3 + 6n2 + 7n - 12)/6 for n = 1, 2, 3, ...
The series appears to be alternating between adding and subtracting numbers. The pattern seems to be adding 1, then subtracting 2, then adding 3, and finally subtracting 4. Following this pattern, the next number in the series would be 1 (subtracting 4 from -1).