I am working on an algorithm to count the number of models for Exactly One in Three SAT (X3SAT) instances. It is known that a chain of X3SAT clauses of length $c$ has $F(c+3)$ satisfying assignments where $F(x)$ is the Fibonacci series. A chain of length $c$ must have $2c+1$ distinct literals. Making some completely unwarranted assumptions about the number of disjoint chains of length $c$ that will "cover" an X3SAT instance I get the following relation:
$F(c+3)^k$ where $k=n/(2c+1)$
Can this function be simplified? Can it be rewritten in a form like $g(c)^n$?