How many ways can the integers 1,1,2,3,4,5,6 be arranged in a row, so that no integer is immediately adjacent to two strictly larger integers?
NOTE: The sequence 3,1,2,4,5,6,1 is not valid as 1 is adjacent to 2 and 3, both of which are strictly larger than 1.
The sequence 3,1,1,2,4,5,6, satisfies the conditions of the question.