What kind of degree is allowed? Since you've given 4 points, a cubic polynomial would fit perfectly: (according to Wolfram Alpha)
Change cubic to quadratic or linear in the above link to get lower degree fits (quadratic also comes pretty close).
Thanks for your reply. I intentionally left it open for various options.
How about this: Find the "best fit" equation for the data:
(0,1),(1,4),(2,13),(3,40),(4,121),(5,364) but not a polynomial equation,
since there is always one with perfect fit if the degree is not restricted and
the set is finite. (some variation of an exponential equation)