Madeline likes baking, perhaps a bit too much, which means she sometimes needs to prepare starter for it$.$ Each day she will Prepare a starter, Bake a loaf of bread, or just Relax. Her only rule is that she never Relaxes on $3$ or more days in a row.

Let an represent the number of ways Madeline can act across n days $($where n $>=0).$

$($a$)$ Find a recurrence relation for an$.$

$($b$)$ What are the initial conditions for the recurrence relation from part $($a$)?$ Only give the minimum required number of initial conditions.