= Solution
For a nonzero <geometric sequence>, substitute $H_n=cq^n$ into the <linear recurrence> and cancel $cq^{n-1}$:
$$
q^2=q+1.
$$
The <characteristic equation of a linear recurrence> therefore has roots
$$
\boxed{q=\phi=\frac{1+\sqrt5}{2}\quad\text{or}\quad
q=\psi=\frac{1-\sqrt5}{2}.}
$$
The zero <sequence> $c=0$ is a degenerate solution for any $q$ for which the displayed expression is defined. A nonzero <sequence> with $q=0$ cannot satisfy the recurrence at $n=1$, since it would require $0=0+H_0$.
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