A student can do the things bellow: a. Do his homework in 2 days b. Write a poem in 2 days c. Go on a trip for 2 days d. Study for exams for 1 day e. Play pc games for 1 day A schedule of n days can be completed by any combination of the activities above. For example 3 possible schedules for 7 days are: homework, poem, homework, play poem, study, play, homework, study trip, trip, trip, study Find a recursive function T(n) that represents the number of all possible schedules for n days. I just need a start. Any ideas will be greatly appreciated.

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A student can do the things bellow: a. Do his homework in 2 days b. Write a poem in 2 days c. Go on a trip for 2 days d. Study for exams for 1 day e. Play pc games for 1 day A schedule of n days can be completed by any combination of the activities above. For example 3 possible schedules for 7 days are: homework, poem, homework, play poem, study, play, homework, study trip, trip, trip, study Find a recursive function T(n) that represents the number of all possible schedules for n days. I just need a start. Any ideas will be greatly appreciated.

Mathematics
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Basically you want to find the number of nonnegative integer solutions to below equation \[n=2a+2b+2c+d+e\]
So, T(n)=3T(n-2)+2T(n-1)?
may i know how you got that

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Well to be honest, i don't exactly know how. I have been searching for examples over the net and this is how they write a recursive function. For example, i read this question where there are n steps, and a person can either take 1 step at a time, or 2 steps at a time. We had to tell the number of ways to take n steps. and as you said, the equation that time would be a+2b=n.. and the recursive fucntion they wrote was t(n)=t(n-1)+t(n-2).. so yeah I don't exactly know how. I have been taking this for granted. I'd be very happy if could tell me more about it.
check this http://math.stackexchange.com/questions/614356/difficult-recursion-problem
I checked that out before posting it here. Don't really understand it completely.
suppose \(n=1\), how many ways can you schedule \(1\) day ?
you can either `study` or `play`, so only \(2\) ways, yes ?
that means \[T(1)=2\]
next let \(n=2\) and work the number of ways \(2\) days can be scheduled
I get it now. Thank you very much... also, suppose i don't want the duplicates.. like, i treat "poem, study, play, homework, study" and "study, poem, play, homework, study" the same... how do I draft an algo for that? @ganeshie8
no idea how you can even solve this its more of an opinion than a math question.

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