What is the nth term for the sequence 11 12 15 16 19 20 21 24 25 26 29 30 31 32, and what is the nth term formula?

The sequence you've posted seems to be following a pattern based on ones and threes in sets of two. With each new set, the amount of times the number is increased by one increases, while the amount of times the number is increased by three remains the same. Look at the following chart:

#       Add
11      +1
12      +3
15      +1
16      +3
19      +1
20      +1
21      +3
24      +1
25      +1
26      +3
29      +1
30      +1
31      +1
32

The first set is "plus one, plus three | plus one, plus three." The next is "plus one, plus one, plus three | plus one, plus one, plus three." The third set begins "plus one, plus one, plus one," and we can assume that the next numbers would be "plus three | plus one, plus one, plus one, plus three." Finishing that out, the next numbers would look like:

#       Add
11      +1
12      +3
15      +1
16      +3
19      +1
20      +1
21      +3
24      +1
25      +1
26      +3
29      +1
30      +1
31      +1
32      +3
35      +1
36      +1
37      +1
38      +3
41

To continue, you would now need to add one four times. "Plus one, plus one, plus one, plus one, plus three | plus one, plus one, plus one, plus one, plus three." And so on... hope this helps!