For all n, the following holds: A213708(n) <= A179016(n) <= A173601(n). This sequence gives the distance of the node n in the infinite trunk of beanstalk (A179016(n)) from the lesser edge of the A086876(n) wide window which it at that point must pass through.

The increasing steps seem to be quite constrained in their magnitude, compared to the decreasing steps. (This depends on how the "tendrils", i.e. the finite side-trees on the other side of the infinite trunk grow and reach their tops).