Soldering Robot with a Repeat Limit

A soldering robot travels across a circuit board from pad (0,0)(0,0) to pad (7,4)(7,4), moving one unit at a time either right (R)(R) or up (U)(U). Its firmware refuses to execute the same direction three times consecutively — at most two identical moves may occur in a row. How many move-sequences satisfy this constraint?

Answer

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