User blog:ChromaticiT/Cross function

Let's play a game called Crossings.

Every game starts on an empty, infinite neighborhood, with some shops. The ideal Crossings game is one in which the maximal number of moves has been reached. The starting and any subsequent shops may be anywhere.

A "move" is drawing a road between two points. If you ever draw a line that results in an intersection, or crossing, between roads, add [n] new shops to the neighborhood where [n] is the number of intersections created. Any roads that have a crossing are considered abandoned. Any new roads cannot intersect an abandoned road. The game ends when there are no more possible moves.

The Crossing function is defined like so.

Let #(x) be the maximal number of moves for a game starting with [x] shops. I need some help. What's the growth rate? And more importantly, is #(5) finite?
 * 1) (1) = 0
 * 2) (2) = 1
 * 3) (3) = 3
 * 4) (4) = 10