3,-6,12,4,20,

The first term is 3, to start with.
To get from 3 to -6, subtract 9
To get from -6 to 12, add 18, (which is twice 9, which is twice what we just subtracted)
To get from 12 to 4, subtract 8, (which is 1 less than what we last subtracted)
To get from 4 to 20, add 16, (which is twice 8, which is twice what we just subtracted.)

So we start with 3, then the pattern is:

subtract 9, add 18, subtract 8, add 16,


A. To get an even numbered term from the preceding odd-numbered term,
the pattern is subtract 9, subtract 8, etc.

B. To get from an odd-numbered term from the preceding even-numbered term,
the rule is: add twice what we just subtracted.

To get the next term, which is the 6th term, an even-numbered term, we use 
rule A and subtract 1 less than what we last subtracted, or 7, and get 13.

To get the next term, which is the 7th term, an odd numbered term, we use
rule B and add twice what we just subtracted, or 2×7 or 14, and get 27.

Here are the first 10 terms:

1.  3
2.  -6
3.  12
4.  4
5.  20
6.  13
7.  27
8.  21
9.  33
10. 28

Edwin