If

$$

$$is a bit string, let

$$

$($

$$

$)$

$$be the maximum number of consec

$-$

utive

$0$

$\text{'}$

s in

$$

$.$

$[$

Examples:

$$

$($

$1$

$0$

$0$

$1$

$0$

$)$

$=$

$2$

$,$

$$

$($

$0$

$0$

$1$

$1$

$0$

$0$

$0$

$1$

$)$

$=$

$3$

$.$

$]$

Let

$$

$$

$$be the number of

$$

$-$

bit strings

$$

$$with

$$

$($

$$

$)$

$<=$

$2$

$.$

Develop a recurrence relation for

$$

$1$

$,$

$$

$2$

$,$

dots.