Generally speaking, adjacent means next to:
My house was adjacent to his. But is does not necessarily imply they were touching. But it can.
Objects can be arranged in sequence or sequentially =in an ordered manner. As long as the pattern repeats. The sequence (adverb: sequentially) is whatever order you wish impose on objects. That said, if all the objects are the same thing, sequence does not work so well.
Continuous or continuous refers to time, usually, something that does not stop (continuous production). Or something that goes on unbroken for some length: There is a continuous line (as opposed to discontinuous) drawn on the map between point A and point B.
For those boxes in the picture, I would say:
the boxes are placed (one after the other) in sequence or sequentially on a line.