10 chairs are arranged in a circle. Then the number of subset of this set of chairs that contain at least three adjacent chairs is N, then the value of N

As a subset with less than 3 chairs cannot contain 3 adjacent chair, these are only 10
sets of 3 chairs so that they are all 3 adjacent there are 10 subsets of 4 chairs where all r
adjacent and
10 x 5 =50, where there are only 3
If there are 5chairs,10 have all 5 adjacent 10 x 4 = 40 have 4 adjacent and 
$10x^5{C}_2=100$ have
3 adjacent with 6 chairs in the subset
10 have all 6 adjacent, 10 x 3= 30 have 5 adjacent $10{\times }^4{C}_2=60$ have 4 adjacent $\frac{10\times 3}{2}=15$ have 2 groups of 3 adjacent chairs and $10\times \left({ }^5{C}_2-3\right)=70$ have 1
group of 3 adjacent chairs. All possible subsets with more than 6 chairs have at least 1
group of 3 adjacent.
So adding all it is total= 581