Strange square brackets in recurrence equation

Question

I have the following recurrence given:

$$a_{0}=1$$ $$a_{1}=1$$ $$a_{n}=3a_{n-2}+3a_{n-1}$$

Why is that equal to something like this?:

$$a_{n}=3a_{n-2}+3a_{n-1}-2[n=1]+[n=0 ]$$

What are those brackets?

Answer 1

These are most likely Iverson Brackets. If the Boolean expression inside the square bracket is true, then the bracket evaluates to $1$. Otherwise, the bracket evaluates to $0$.