Help finding pattern or equation from maths investigation?

[Melly]

There are three different bugs: happy, sad and blank. Only one bug is needed to reporduced and each generation of bugs gives birth to two new bugs and dies immediately.

- A happy bug produces a sad bug and a blank bug
- A sad bug produces two happy bugs
- A blank bug produces a happy and a sad bug
- Each eneration lasts exactly the same length of time
- In the beginning there was only one happy bug

Gen Happy Sad Blank Total No. Bugs
11--1
2-112
331-4
42338
595216
61211932
731211264
8544331128
91178554256
10224171117512
114593412241024
129066834592048
13182513659064096
143636273118258192
1572875461363616384
161455810923728732768
1729133218451455865536
Then it said calculate the probability of choosing a happy sad or blank bug from each generation and ulitmately any generation. And i got this...

Gen Happy Sad Blank

1 1 0 0
2 0 0.5 0.5
3 0.75 0.25 0
4 0.25 0.375 0.375
5 0.563 0.313 0.125
6 0.375 0.344 0.281
7 0.484 0.328 0.188
8 0.422 0.336 0.242
9 0.457 0.332 0.211
10 0.438 0.334 0.229
11 0.448 0.333 0.219
12 0.442 0.333 0.224
13 0.446 0.333 0.221
14 0.444 0.333 0.223
15 0.445 0.333 0.222
16 0.444 0.333 0.222
17 0.445 0.333 0.222

I dont see a pattern or how to find an equation to find the probabilty from any generation. Can you help?
my columns didnt come out very clear