As the leader of a popular indie math rock group, you would like to hold a concert. A concert consists of a number of songs played in sequence, followed by a period of reflection.
The reflection lasts 0 or more minutes, in which the musicians sit on stage staring at the audience, who are invited to meditate on the proceedings.
You have the following songs available:
â€œFaerieâ€™s Aire and Death Waltzâ€ (4m)
â€œDuetto Boffo di Due Gattiâ€ (4m)
â€œThree Minute Songâ€ (3m)
â€œHot Patootie – Bless My Soulâ€ (3m)
â€œI Cannot Be Played On Record Player 1â€ (2m)
Each song is listed with its duration (in minutes). After one song finishes, the next (if any) immediately begins.
For example, some possible concerts which last (exactly) 7 minutes:
â€œFaerieâ€™s Aireâ€, â€œThree Minute Songâ€, 0 minutes of reflection
â€œThree Minute Songâ€, â€œFaerieâ€™s Aireâ€, 0 minutes of reflection
â€œDuetto Boffoâ€, â€œI Cannot Be Played On Record Player 1â€, 1 minute of reflection
â€œHot Patootieâ€, â€œHot Patootieâ€, 1 minute of reflection
â€œI Cannot Be Played On Record Player 1â€, 5 minutes of reflection
7 minutes of reflection
Find a recurrence and appropriate initial conditions for the number of concerts which last
(exactly) n minutes, n â‰¥ 0.
Give a brief justification why your recurrence is correct.
(no justification = no credit)
For your initial conditions, use as many as you need, but no more.