Context free Grammar

[Binx]

im trying to create a context free grammar over the language

 

L = {a, b}

 

where b is never trippled

 

Here is what I have so far

S-> X | Y

X-> bbXY | aX | aY | bb

Y-> b | lamda

 

lamda being the empty letter

 

I'm wondering if this is an acceptable solution, I guess im also not sure if b never being trippled means it also cannot be quadrupled which would make the problem easier I suppose.