Music on the planet Alpha Lyra IV consists of only two notes, called A and B. Also, songs never include three consecutive repetitions of any sequence nor does BB ever occur. A sequence of notes can have 1 or more notes in it.

What is the longest song on Alpha Lyra IV?

In increasing number of notes in a song, the following songs are possible for each

One note
a
b

Two notes
aa
ab

Three notes
aab
aba
baa
bab

Four notes
aaba
abaa
abab
baab
baba

Five notes
aabaa
aabab
abaab
ababa
baaba
babaa
babab

Six notes
aabaab
aababa
abaaba
ababaa
baabaa
baabab
babaab

Seven notes
aabaaba
aababaa
aababab
abaabaa
abaabab
ababaab
baabaab
baababa
babaaba

Eight notes

aabaabaa
aabaabab
aababaab
abaabaab
abaababa
ababaaba
baabaaba
baababaa
baababab
babaabaa
babaabab

Nine notes

aabaababa
aababaaba
abaababaa
abaababab
ababaabaa
ababaabab
baabaabab
baababaab
babaabaab
babaababa

Ten notes
aabaababaa
aabaababab
aababaabaa
aababaabab
abaababaab
ababaabaab
ababaababa
baabaababa
baababaaba
babaabaaba
babaababaa

Edited on December 14, 2004, 2:54 pm

Posted by Syzygy on 2004-12-14 14:41:55