discreet math find a recurrence and appropriate initial conditions

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:

“Faerie’s Aire and Death Waltz” (4m)

“Duetto Boffo di Due Gatti” (4m)

“Three Minute Song” (3m)

“Hot Patootie – Bless My Soul” (3m)

“I Cannot Be Played On Record Player 1” (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:

“Faerie’s Aire”, “Three Minute Song”, 0 minutes of reflection

“Three Minute Song”, “Faerie’s Aire”, 0 minutes of reflection

“Duetto Boffo”, “I Cannot Be Played On Record Player 1”, 1 minute of reflection

“Hot Patootie”, “Hot Patootie”, 1 minute of reflection

“I Cannot Be Played On Record Player 1”, 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 ≥ 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.

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