Recurrence relation with a number value (not n)
The recursion tree corresponds to repeated expansion of the recurrence:
$$
\begin{align*}
T(n) &amp;= 3 + aT(n/4) \\ &amp;=
3 + 3a + a^2T(n/16) \\ &amp;=
3 + 3a + 3a^2 + a^3T(n/64) \\ &amp;= \cdots \\ &amp;=
3 + 3a + \cdots + 3a^{k-1} + a^kT(n/4^k) \\ &amp;=
3\frac{a^k-1}{a-1} + a^kT(n/4^k).
\end{align*}
$$
This is the result if you stop the recursion after $k$ steps. If, for example, you define $T(1) = 3$ then for $n = 4^k$ you will get $T(n) = 3+3a+\cdots+3a^k = 3\frac{a^{k+1}-1}{a-1} = \Theta(a^{\log_4 n})$.