4
The next term is -2.
4
16' then 25 and then 36 et.seq. The clue is 0,1,4,9,16,25,36, ... = 0^(2) , 1(2) , 2^(2), 3^(2) , 4^(2) , 5^(2) , 6^(2), ... n^(2) ...
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' then 25 and then 36 et.seq. The clue is 0,1,4,9,16,25,36, ... = 0^(2) , 1(2) , 2^(2), 3^(2) , 4^(2) , 5^(2) , 6^(2), ... n^(2) ...
5.
add 2, add 4, take away 3. I don't know if it has a name.
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).