Binary Concatenations

How many strings of length 8 are there that can be formed by concatenating strings of the form "0", "10" and "11"?

Note: Each of the strings "0", "10" and "11" could be used several times. For example, we can concatenate "0", "10", "10", "0", "10", "10", "0", "0", "10" to get "01010010100010", a string of length 14.

Details and assumptions

String concatenation refers to joining 2 (or more) strings end-to-end, and treated as 1 string. For example, if we concatenate the string "Brilli" of length 6 and string "ant" of length 3, we get the string "Brilliant" of length 9.

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