Suppose you were given a linear, homogeneous recurrence relation of order 5 and that its roots were 2, 3, 3, 3, and 4. What is the closed formula for this recurrence relation?
$a_n = a \cdot 2^n + b \cdot 3^n + c \cdot n \cdot 3^n$ for $n \ge 0$
directions for entering your answer:
\begin{itemize}
\item for unknown coefficients, use a, b, c, etc
\item don't try to solve for these coefficients
\item use the roots in the order they're listed
\item don't use spaces or parentheses
\item do use * for multiplication
\end{itemize}
Answer 1:
a*2^n+b*3^n+c*n*3^n+d*n^2*3^n+e*4^n
