A note on the number of edges of the Jaco Graph, $J_n(1), n \in \Bbb N

Abstract: Kok et.al. [3] introduced Jaco Graphs \emph{(order 1)}. It is hoped that as a special case, a closed formula can be found for the number of edges of a finite Jaco Graph $J_n(1)$. However, the algorithms discussed in Ahlbach et.al. [1] suggest this might not be possible. Finding a closed formula for the number of edges of a Jaco Graph $J_n(1), n \in \Bbb N$ remains an interesting open problem. In this note we present three alternative, \emph{formula}.