I'm trying to find the number of distinct 10-length sequences that contain at least 5 consecutive 1s or 0s.

My thoughts: For precisely 5 consecutive 1s, we have:
111110xxxx
0111110xxx
x0111110xx
xx0111110x
xxx0111110
xxxx011111

(where X can be either 1 or 0). There are $2^4+2^3+2^3+2^3+2^3+2^4 = 64$ combinations.

For 6 consecutive 1s:
1111110xxx
01111110xx
x01111110x
xx0111111x
xxx0111111

Total = 32

For 7 1s:
11111110xx
011111110x
x011111110
xx01111111

Total combinations = 12

For 8 1s:
111111110x
0111111110
x011111111

Total combinations = 5

For 9 1s:
1111111110
0111111111

Total combinations = 2

For 10 1s:

Total combinations = 1

If we add up all the combinations, we get 116 combinations. Now, we can A or B with at least 5 consecutive occurrences, so we multiply this by 2 to give 232.

However, the actual answer is 222, and I don't know why my method isn't working.