A Sequence of Sequences
This research was supported in part by a grant from the Universal Walloons and by a grant from the Ants of America. We thank them for their help. Neither this infinite sequence of sequences nor any of the component sequences (which are all finite) is an unfolding sequence, but you will notice reminiscent properties. How is this generated? For component S( n ), consider all words composed of "1" and "2" of length 0- n . Left justify. Sort. S( n ) is the lengths of the words in sorted order. Thus S(2): Possible words are -,1,2,11,12,21,22. In sorted order, they are -,1,11,12,2,21,22. Their lengths comprising S(2) are 0,1,2,2,1,2,2. 0....................................................................0- 0 011..................................................................0- 2 0122122..............................................................0- 6 012332331233233......................................................0- 14 0123443442344344123443442344344...........