Let a(n) be the number of song sequences you can listen to with 50n cents; you want to find a recurrence for a(n).

How many song sequences can you listen to if n=1?

If you knew how to find a(1), a(2), .... , a(n), how could you compute a(n+1)?

It may help to consider two cases: (1) the n+1st song is a pop song; (2) the n+1st song is a rock song.