the idea being, the notation is for a "serie" or sequence.
f(n-1) simply means, "the value of the term before the current one", whilst "n" is the current term.
[tex]\bf \begin{array}{llll}
term&value\\
------&------\\
f(1)&-3\\\\
f(\stackrel{n}{2})&4[f(\stackrel{n}{2}-1)]+3[f(\stackrel{n}{2}-1)]\\
&4[f(1)]+3[f(1)]\\
&4(-3)+3(-3)\\
&-21\\\\
f(\stackrel{n}{3})&4[f(\stackrel{n}{3}-1)]+3[f(\stackrel{n}{3}-1)]\\
&4[f(2)]+3[f(2)]\\
&4(-21)+3(-21)\\
&-147\\\\
\end{array}[/tex]
[tex]\bf \begin{array}{llll}
&\\
~~~~~~~~~~~~&~~~~~~~~~~~~\\
f(\stackrel{n}{4})&4[f(\stackrel{n}{4}-1)]+3[f(\stackrel{n}{4}-1)]\\
&4[f(3)]+3[f(3)]\\
&4(-147)+3(-147)\\
&-1029\\\\
f(\stackrel{n}{5})&4[f(\stackrel{n}{5}-1)]+3[f(\stackrel{n}{5}-1)]\\
&4[f(5)]+3[f(4)]\\
&4(-1029)+3(-1029)\\
\end{array}[/tex]
