Resistance distance in bent linear 2-trees

In this note we consider the bent linear 2-tree and provide an explicit formula for the resistance distance $r_{G_n}(1,n)$ between the first and last vertices of the graph. We call the graph $G_n$ with vertex set $V(G_n) = { 1, 2, \ldots, n}$and${i,j} \in E(G_n)$ifandonlyif$0<|i-j| \leq 2$ a straight linear 2-tree. We define the graph $H_n$ with $V(H_n)=V(G_n)$ and $E(H_n)=(E(G_n)\cup \{k,k+3\})\setminus (\{k+1,k+3\}$ to be a bent linear 2-tree with bend at vertex $k$.