  The main contribution of this paper is a six-step semi-automatic algorithm
that obtains a recursion satisfied by a family of determinants by
systematically and iteratively applying Laplace expansion to the underlying
matrix family. The recursion allows explicit computation of the Binet form
providing a closed formula for resistance distance between two specified nodes
in a family of graphs. This approach is particularly suited for graph families
with complex structures; the method is used to prove the 1 over 14 conjectured
asymptotic formula for linear 3--trees. Additionally, although the literature
on recursive formulas for resistance distances is quite large, the Fibonacci
Quarterly and the Proceedings have almost no such results despite the fact that
many recursions related to resistance distances involve the Fibonacci numbers.
Therefore, a secondary purpose of the paper is to provide a brief introductory
survey of graph families, accompanied by figures, Laplacian matrices, and
typical recursive results, supported by a modest bibliography of current papers
on many relevant graph families, in the hope to involve Fibonaccians in this
active and beautiful field.
