For the sequence to be non-decreasing, 0 has to take the first place as it has the lowest absolute value. For other integers, a and  –a can arrange in two ways for each a=1,2,3…10.

To explain the point 0, 1, -1 and 0, -1, 1 both are valid sequences. Similarly for all integers, hence we get 2x2x2x…2=2¹⁰ ways=1024 sequences.

Hence option 2.