I have been trying to make a general formula/function that helps in calculating the number of pentagons that may be formed using 2 or more hexagons. Like it is shown in the picture below:
In Fig. 1 there are 2 hexagons and 6 pentagons. Therefore, the ratio becomes $1:3$. However, this should never be the ratio as no pentagon can be formed with a single hexagon. Let $y$ be the number of pentagons formed and $x$ be the number of hexagons, we can say: $y = 3x$ when $x =2$.
In Fig. 2 there are 3 hexagons and 12 pentagons. Therefore, the ratio becomes $1:4$ Now, in this case the equation becomes: $y = 4x$ when $x = 3$.
If we bring in another hexagon, we shall have 6 more pentagons. So, in that case, the ratio will be $2:9$, thereby, changing the equation too. What I mean to say is the ratio is changing every time we introduce a hexagon.
I know that $x$ (number of hexagons) and $y$ (number of hexagons) $\epsilon$ $N$; and $x \geq 2$, $y \geq 6$.
Since the ratios are changing every time we introduce a hexagon, I don't seem to define a general formula of a function that gives us the number of pentagons if we have the number of hexagons. Maybe, I am missing out something.
So the question: How to define a function that gives us the number of pentagons formed in between two or more hexagons?