00:01
In this problem, we have to figure out a recurrence relation for the number of all bit strings of length n that don't contain any consecutive zeros.
00:11
So suppose, let's denote by a .n.
00:15
Bit strings, the number of bit strings of length n is not containing any consecutive zeros.
00:27
Then let's consider the case when n equals 1.
00:31
Then we just have a string of length 1.
00:34
And we have two choices for those strings, 0 or 1.
00:41
So we have a1 equals 2.
00:45
And then a2 comes out to be 3y because we have all bit strings of length 2.
00:54
And there are four such strings because each place has two choices, 0 or 1.
01:00
But we have to exclude the string 0 -0, because we can't have.
01:05
Have two consecutive zeros.
01:06
So a2 comes out to be 4 minus 1, which is 3...