Jarred

There is an on-line resource that explores integer sequences:
http://www.research.att.com/~njas/sequences/
One interesting observation is that A recursive formula may not be unique. Some may be simpler than others, but there must be a number of them (which will give different number values as you go further out). The site gives 95 answers for your numbers!

All of that said, there is a simpler set of numbers which is probably was in the experience of the person who gave you this assignment. To find the formula, try taking first differences:

3		6		10		15		21
	3		4		5		6

and perhaps second differences:

3		6		10		15		21
	3		4		5		6
		1		1		1

These match the first of the 95 answers on the site I mentioned.
As a project, try looking at the bigger ideas for which this is an example.

Walter Whiteley