How many sequences of 0s and 1s are there of length 10 such that there are no three 0s or 1s consecutively anywhere in the sequence?
Solution
We can have blocks of either 1 or 20s and 1s, and these blocks must be alternating between 0s and 1s. The number of ways of arranging blocks to form a sequence of length is the same as the number of omino tilings of a rectangle, and we may start each sequence with a 0 or a 1, making or, in this case, 178 sequences.
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