Suppose we have $$H(n) = H(n-1)-H(n-2) \rightarrow x^2-x+1 \rightarrow r_1 = \frac{1+\sqrt{-3}}{2}, r_2 = \frac{1-\sqrt{-3}}{2}$$
or
$$H(n) = H(n-1)+H(n-2)+H(n-3) \rightarrow x^3-x^2-x-1=0$$
In either case, how would the recurrence relation be solved? Are there other techniques for complex roots/non-quadratics?