MathDB

We define a beehive of order

n

as follows:
a beehive of order 1 is one hexagon
To construct a beehive of order

n

, take a beehive of order

n-1

and draw a layer of hexagons in the exterior of these hexagons. See diagram for examples of

n=2,3

Initially some hexagons are infected by a virus. If a hexagon has been infected, it will always be infected. Otherwise, it will be infected if at least 5 out of the 6 neighbours are infected.
Let

f(n)

be the minimum number of infected hexagons in the beginning so that after a finite time, all hexagons become infected. Find

f(n)

Problem Statement