1,3

Definition of a canonical minimal transition-complete sequence, by example: If n=3, then 2123132312132312 is a transition-complete sequence because each element (1,2, or 3) is followed by each other element at least once.

3132123 is a minimal transition complete sequence, as each element is followed by each other element EXACTLY once.

1231321 is a canonical minimal transition-complete sequence because 1 appears before the first appearance of 2 and 2 appears before the first appearance of 3.

With n=1, there is only the possibility "1". With n=2, there is only the possibility "121". With n=3, there are the following 3 possibilities: "1213231", "1231321" and "1232131". Here is one of the 128 possibilities with n=4: "1231342143241" With n=5, I think there are over 120000 possibilities and at n=6 there may be a large number.

Sequence in context: A041867 A134711 A163850 this_sequence A123047 A097420 A037119

Adjacent sequences: A108710 A108711 A108712 this_sequence A108714 A108715 A108716

nonn,more,nice

Philipp G. Blume (pgblu(AT)hotmail.com), Jun 20 2005