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*You own an iPod on which you currently have 19 songs loaded. You wish to create a playlist in which no two consecutive songs are played, no more than two songs in a row are omitted, and the songs are played in the order they are currently loaded. How many playlists are possible?*

Our method was to figure out how many were possible on less number of songs, such as 3, 5, 7 etc., and find a pattern. The number of possible playlists for 3 songs is 4, for 5 it's 7, for 7 it's 12, for 9 it's 21, and for 11 it's 36. These numbers were found by counting out every individual possibility. We then looked for a pattern within these numbers. We found that by adding 3 to the possibilities of 3, we received the number for 5 songs. Then adding 5 (2 more than the previous addition), we received the number for 7 songs. Than adding 9 (4 more than the previous), receiving the number for 9 songs. then 15 (6 more than the previous), we received the number for 11 songs. The number added goes up by 2 each consecutive time, and we applied this formula to get the rest of the numbers, for 13, 15, 17 and 19. However, I do not think that our number (196) is large enough. Anyone have thoughts? Are we correct? Or why is our method wrong (if it is). Huge appreciation for help received before tomorrow afternoon. Thanks in advance.