Genetics Challenge!

Note: You need to know how to make double punnett squares to do this challenge. Check out this article about a dihybrid cross, which is a double punnett square in simple terms. A gamete is a sex cell, just so you know.

You are a florist who has just recieved a massive order of red, thornless roses. While trying to explain to your customer that roses don't normally come without thorns and that he will have to pay an extra fee, you realize that your latest blooms of white roses do not have any thorns. You have decided to experiment to try to create red roses without thorns. Currently, you have one bush of pink roses with thorns and one bush of white roses without thorns.

FACTS:

Red and white alleles show incomplete dominance
Thorns are a dominant trait
Your pink roses have only thorn alleles
Each bush produces four roses
Each rose produces enough seeds to successfully grow eight bushes
Roses die after producing seeds
Roses can fertilize another rose and produce seeds
To keep things simple, one rose can only fertilize one other rose
You can grow three generations

How many red thornless roses can you grow?

Once you get an answer, post it as a comment to see how many we can grow! And if you find it daunting (like me, even though I made it up for myself) try it anyway. I'm curious to see what what happens.