All sequences with 19 element

[xyzzyx]

Hello!
I am a math student and I can't solve this task.
Set S consists of all sequences with 19 elements which satisfy these conditions:
a) every element is 0 or 1
b) first and last element of every sequence is 0
c) there is no sequence of numbers with two adjacent 0
d) there is no sequence of numbers with three adjacent 1
Thanks in advance!
I am one of the best junior math competitor in my country in my category.

 

[pka]

I am new member of this community and if anyone annoys me about my question I will block him and delete his comment.

Welcome and please follow this link. Hope we can help.

 

[Steven G]

I read your post twice and did not see any question asked.