Tower of Hanoi confusion from Concrete Mathematics so I just started reading Concrete Mathematics as a precursor to The Art of Computer Programming vol. 1. I'm on page 3 and I'm already struggling. Anyway, the recurrence is stated to be:
$2T_{n-1} +1$
But I don't understand how this works. If $n$ is 3, then we would have:
$2T_{3-1}+1$ 
or 
$2(2) + 1 = 4$
correct? But that's not right. The answer here is 7. They go on to compute it saying:
$T_3 = 2 * 3 + 1 = 7; T_4 = 2*7+1=15$
Now the $T_4$ one makes a little bit of sense if you calculate $2*4 - 1$ instead of $2*(4-1)$, but that logic doesn't seem to apply to that one. I'm trying to figure out of it's a range of $n$ to $1$, but $2*(3*2*1) + 1 = 13$ so obviously that's not right...
Oh, maybe I've got it. I'm substituting $2T_{n-1}$ with $2(n-3)$ when I'm actually supposed to use the result of $T_{n-1}$ instead and multiply that by 2 and add 1.
Thanks in advance. 

Hint:
$T_1=\color{#C00}{1}$
$T_2=2T_1+1=2\cdot\color{#C00}{1}+1=\color{#090}{3}$
$T_3=2T_2+1=2\cdot\color{#090}{3}+1=\color{#00F}{7}$
$T_4=2T_3+1=2\cdot\color{#00F}{7}+1=15$  
