The next term is -2.
4
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, ...
456789
The next term is -2.
1, 2, 0, 3, -1, 4, -2, 5, -3, 6
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
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, ...
4