Consider the sequence Fo$,$ F$1,$ F$2,...,$ defined recursively as follows:

Fn$-1$Xn$+$n$$

n $=1$

n $>1.$

$(1)$ Please write a pseudocode to compute En using a recursive function and show its recurrence relation and big O notation.

$(2)$ Please write a pseudocode to compute Fn using a for loop.

$(10$ points$)$