Finding a solution to the following conditions? So for these 5 conditions, I am trying to find the solution/formula for them. 
What would $a_n$ equal basically? If it helps, the recurrence relation these 5 conditions were generated from was $a_n = a_{n - 1} + 2n$.   Any help would be greatly appreciated. 

$$
\begin{align*}
a_0 &amp;= 4 \\
a_1 &amp;=  6 \\
a_2 &amp;= 10 \\
a_3 &amp;= 16 \\
a_4 &amp;= 24
\end{align*}
$$
There are infinitely many sequences starting $4,6,10,16,24$. If I understand you correctly, this sequence was generating according to the rule $a_n = a_{n-1} + 2n$ with the initial value $a_0 = 4$. In that case, you have
$$
a_n = a_0 + \sum_{k=1}^n (2k) = a_0 + 2 \frac{n(n+1)}{2} = n^2 + n + 4.
$$