> #ATTENDANCE QUIZ FOR LECTURE 22
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> #THE NUMBER OF ATTENDANCE QUESTIONS WERE: 8
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> 
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> #Q1
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> #Write the above proof (if possible with more details) in your own words.
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> 
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> #If we have a tree with 1 vertex, it should have 0 edge, n-(n-1) = 1- 0 = 1
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> #proved
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> 
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> #Q2
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> #What is the OEIS A number of this sequence?
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> #[1,1,3,16,125,1296,16807...]
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> 
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> #A000272
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> 
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> #Q3
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> #Is this sequence ([0,0,1,15,222,3660, 68295...]) in the OEIS? If yes, what is the A-Number?
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> 
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> #YES
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> #THE A NUMBER IS A057500

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> #Q4
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> #What is the smallest r such that ATreeSeq(30,r) is not in the OEIS? Optional: Submit it! 
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> 
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> #When r=13,ATreeSeq(30,r) is not in the OEIS
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> 
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> #Q5
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> #What is the ratio of the time it takes between time(TreeSeq(75)); and time(TreeSeq1(75));? 
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> 
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> #time(TreeSeq(75))/time(TreeSeq1(75))
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> 
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> #Q6
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> # Let r_e(n) be the number of roots trees where every vertex has an even number of children. Set up a functional equation for egf of r_e(n).What are the first 20 terms of this sequence? Is it in the OEIS?

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> #Q7
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> #How many labelled trees are there with 27 vertices and 6 leaves?
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> 
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> #coeff(TreeSeqL(27, t)[27], t, 6)
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> #5466338131409680923049107456000000

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> 
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> #Q8
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> #Conjecture an explicit formula for the average number of leaves of a labeled trees with n vertices.
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> #A bigger challenge: What is the limit if you divide by n
> An even bigger challenge: prove the conjecture
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