  The Exact Satisfiability problem, XSAT, is defined as the problem of finding
a satisfying assignment to a formula in CNF such that there is exactly one
literal in each clause assigned to be 1 and the other literals in the same
clause are set to 0. If we restrict the length of each clause to be at most 3
literals, then it is known as the X3SAT problem. In this paper, we consider the
problem of counting the number of satisfying assignments to the X3SAT problem,
which is also known as #X3SAT.
  The current state of the art exact algorithm to solve #X3SAT is given by
Dahll\"of, Jonsson and Beigel and runs in $O(1.1487^n)$, where $n$ is the
number of variables in the formula. In this paper, we propose an exact
algorithm for the #X3SAT problem that runs in $O(1.1120^n)$ with very few
branching cases to consider, by using a result from Monien and Preis to give us
a bisection width for graphs with at most degree 3.
